Some useful layered cross product decompositons are derived both for general bit permutation networks and for(2n-1)-stage multistage interconnection networks.Several issues in related works are clarified and the rearr...Some useful layered cross product decompositons are derived both for general bit permutation networks and for(2n-1)-stage multistage interconnection networks.Several issues in related works are clarified and the rearrangeability of some interesting networks are considered.In particular, the rearrangeability of one class of networks is formulated as a new type of combinatorial design problmes.展开更多
The reliability of a network is an important indicator for maintaining communication and ensuring its stable operation. Therefore, the assessment of reliability in underlying interconnection networks has become an inc...The reliability of a network is an important indicator for maintaining communication and ensuring its stable operation. Therefore, the assessment of reliability in underlying interconnection networks has become an increasingly important research issue. However, at present, the reliability assessment of many interconnected networks is not yet accurate,which inevitably weakens their fault tolerance and diagnostic capabilities. To improve network reliability,researchers have proposed various methods and strategies for precise assessment. This paper introduces a novel family of interconnection networks called general matching composed networks(gMCNs), which is based on the common characteristics of network topology structure. After analyzing the topological properties of gMCNs, we establish a relationship between super connectivity and conditional diagnosability of gMCNs. Furthermore, we assess the reliability of g MCNs, and determine the conditional diagnosability of many interconnection networks.展开更多
Recent architectures of multi-core systems may have a relatively large number of cores that typically ranges from tens to hundreds;therefore called many-core systems.Such systems require an efficient interconnection n...Recent architectures of multi-core systems may have a relatively large number of cores that typically ranges from tens to hundreds;therefore called many-core systems.Such systems require an efficient interconnection network that tries to address two major problems.First,the overhead of power and area cost and its effect on scalability.Second,high access latency is caused by multiple cores’simultaneous accesses of the same shared module.This paper presents an interconnection scheme called N-conjugate Shuffle Clusters(NCSC)based on multi-core multicluster architecture to reduce the overhead of the just mentioned problems.NCSC eliminated the need for router devices and their complexity and hence reduced the power and area costs.It also resigned and distributed the shared caches across the interconnection network to increase the ability for simultaneous access and hence reduce the access latency.For intra-cluster communication,Multi-port Content Addressable Memory(MPCAM)is used.The experimental results using four clusters and four cores each indicated that the average access latency for a write process is 1.14785±0.04532 ns which is nearly equal to the latency of a write operation in MPCAM.Moreover,it was demonstrated that the average read latency within a cluster is 1.26226±0.090591 ns and around 1.92738±0.139588 ns for read access between cores from different clusters.展开更多
In order to extend the application scope of NDN and realize the transmission of different NDNs across IP networks,a method for interconnecting NDN networks distributed in different areas with IP networks is proposed.F...In order to extend the application scope of NDN and realize the transmission of different NDNs across IP networks,a method for interconnecting NDN networks distributed in different areas with IP networks is proposed.Firstly,the NDN data resource is located by means of the DNS mechanism,and the gateway IP address of the NDN network where the data resource is located is found.Then,the transmission between different NDNs across the IP network is implemented based on the tunnel technology.In addition,in order to achieve efficient and fast NDN data forwarding,we have added a small number of NDN service nodes in the IP network,and proposed an adaptive probabilistic forwarding strategy and a link cost function-based forwarding strategy to make NDN data obtaining the cache service provided by the NDN service node as much as possible.The results of analysis and simulation experiments show that,the interconnectionmethod of NDN across IP network proposed is generally effective and feasible,and the link cost function forwarding strategy is better than the adaptive probability forwarding strategy.展开更多
Connectivity is a vital metric to explore fault tolerance and reliability of network structure based on a graph model. Let be a connected graph. A connected graph G is called supper-κ (resp. supper-λ) if every minim...Connectivity is a vital metric to explore fault tolerance and reliability of network structure based on a graph model. Let be a connected graph. A connected graph G is called supper-κ (resp. supper-λ) if every minimum vertex cut (edge cut) of G is the set of neighbors of some vertex in G. The g-component connectivity of a graph G, denoted by , is the minimum number of vertices whose removal from G results in a disconnected graph with at least g components or a graph with fewer than g vertices. The g-component edge connectivity can be defined similarly. In this paper, we determine the g-component (edge) connectivity of varietal hypercube for small g.展开更多
Most of users are accustomed to utilizing virtual address in their parallel programs running at the scalable high-performance parallel computing systems.Therefore a virtual and physical address translation mechanism i...Most of users are accustomed to utilizing virtual address in their parallel programs running at the scalable high-performance parallel computing systems.Therefore a virtual and physical address translation mechanism is necessary and crucial to bridge the hardware interface and software application.In this paper,a new virtual and physical translation mechanism is proposed,which includes an address validity checker,an address translation cache(ATC),a complete refresh scheme and many reliability designs.The ATC employs a large capacity embedded dynamic random access memory(eDRAM)to meet the high hit ratio requirement.It also can switch the cache and buffer mode to avoid the high latency of accessing the main memory outside.Many tests have been conducted on the real chip,which implements the address translation mechanism.The results show that the ATC has a high hit ratio while running the well-known benchmarks,and additionally demonstrates that the new high-performance mechanism is well designed.展开更多
Unchecked breast cell growth is one of the leading causes of death in women globally and is the cause of breast cancer.The only method to avoid breast cancer-related deaths is through early detection and treatment.The...Unchecked breast cell growth is one of the leading causes of death in women globally and is the cause of breast cancer.The only method to avoid breast cancer-related deaths is through early detection and treatment.The proper classification of malignancies is one of the most significant challenges in the medical industry.Due to their high precision and accuracy,machine learning techniques are extensively employed for identifying and classifying various forms of cancer.Several data mining algorithms were studied and implemented by the author of this review and compared them to the present parameters and accuracy of various algorithms for breast cancer diagnosis such that clinicians might use them to accurately detect cancer cells early on.This article introduces several techniques,including support vector machine(SVM),K star(K∗)classifier,Additive Regression(AR),Back Propagation Neural Network(BP),and Bagging.These algorithms are trained using a set of data that contains tumor parameters from breast cancer patients.Comparing the results,the author found that Support Vector Machine and Bagging had the highest precision and accuracy,respectively.Also,assess the number of studies that provide machine learning techniques for breast cancer detection.展开更多
Diagnosability of a multiprocessor system is one important study topic. In 2012, Peng et al. proposed a measure for fault tolerance of the system, which is called the g-good-neighbor diagnosability that restrains ever...Diagnosability of a multiprocessor system is one important study topic. In 2012, Peng et al. proposed a measure for fault tolerance of the system, which is called the g-good-neighbor diagnosability that restrains every fault-free node containing at least g fault-free neighbors. In 2015, Zhang et al. proposed a measure for fault diagnosis of the system, namely, g-extra diagnosability, which restrains that every fault-free component has at least g+1 fault-free nodes. In this paper, we obtain some properties of the g-good-neighbor (g-extra) diagnosability of the system and give the g-good-neighbor (g-extra) diagnosability of some graphs under the PMC model and MM<sup>*</sup> model.展开更多
Diagnosability of multiprocessor systems is an important research topic.The system and an interconnection network have an underlying topology,which is usually presented by a graph.In 2012,Peng et al.proposed a metric ...Diagnosability of multiprocessor systems is an important research topic.The system and an interconnection network have an underlying topology,which is usually presented by a graph.In 2012,Peng et al.proposed a metric for fault diagnosis of the graph,namely,the n-neighbor diagnosability that restrains every fault-free node to contain at least n fault-free neighbors.It is difficult to get the n-neighbor diagnosability of the graph from the definition of the n-neighbor diagnosability.Afterwards,some sufficient and necessary conditions are given.It is also difficult to find the n-neighbor diagnosability of the graph from those results.In this paper,we show some new sufficient conditions for the graph to be n-neighbor d-diagnosable under the MM*model.It improves the corresponding result of[Theoretical Computer Science 773(2019)107-114].展开更多
Diagnosability of a multiprocessor system is one important study topic.Cayley graph network Cay(T_n,S_n) generated by transposition trees Tnis one of the attractive underlying topologies for the multiprocessor system....Diagnosability of a multiprocessor system is one important study topic.Cayley graph network Cay(T_n,S_n) generated by transposition trees Tnis one of the attractive underlying topologies for the multiprocessor system.In this paper,it is proved that diagnosability of Cay(T_n,S_n) is n-1 under the comparison diagnosis model for n ≥ 4.展开更多
It has long been an outstanding conjecture that any(2^(n)×2^(n))-stage shuffle exchange network(Omega net-work)is rearrangeable for 2n 62n.Many researchers have failed to prove this conjecture,including a recent ...It has long been an outstanding conjecture that any(2^(n)×2^(n))-stage shuffle exchange network(Omega net-work)is rearrangeable for 2n 62n.Many researchers have failed to prove this conjecture,including a recent one established by Hasan.However,nobody has pointed out its fallacy.Therefore,as one of the objectives,this paper shall clarify this fact.Since the case of n 53 has been proven by many researchers[1,2],this paper uses a con-structive approach to prove that when n 54,the 7-stage 16616 shuffle exchange network is also rearrangeable.The paper also presents the model of a balanced tree to avoid internal conflict,the representation of permutations using a connection graph and loop graph,and the con-cepts of symmetry graph and identical transform.Based on graphic composition and bipartition,the permutations 16×16 are divided into five classes,with five assignment algorithms proposed.These algorithms are simpler,clearer and easier to program.The techniques used for n=4 may provide hints for the general case of n>4.展开更多
The accessibility and mass transfer between catalytic sites and substrates/intermediates are essential to a catalyst's overall performance in oxygen electrocatalysis based energy devices.Here,we present an“in-sit...The accessibility and mass transfer between catalytic sites and substrates/intermediates are essential to a catalyst's overall performance in oxygen electrocatalysis based energy devices.Here,we present an“in-situ self-sacrifice template etching strategy”for reconstructing MOF-derived M-N-C catalysts,which introduces micro-meso-macro pores with continuous apertures in a wide range and a central hollowout structure to optimize the electrochemical oxygen redox kinetics.It is realized via one-step pyrolysis of ZIF-8 single crystal epitaxially coating on a multi-functional template of the Fe,Co co-loaded mesoporous ZnO sphere.The ZnO core is reduced during the general pyrolysis of ZIF-8 into M-N-C and acts as a pore former to etch the surrounding ZIF-8 shell into diverse channels anchoring highly exposed Fe and Co-based active sites with edge enrichment.The redesigned catalyst reveals apparent structural benefits towards enhanced oxygen redox kinetics as bifunctional cathode catalysts of rechargeable zinc-air battery compared with the primitive bulk M-N-C catalysts and the mixture of commercial Pt/C and Ir/C.The unique structure-based activity advantages,the omitted template removal step and good template compatibility during synthesis make the strategy universal for the channel engineering of electrocatalysts.展开更多
We consider the problem of existence of a Hamiltonian cycle containing a matching and avoiding some edges in an n-cubc Qn,and obtain the following results.Let n≥3,MСE(Qn),and FСE(Qn)\M with 1≤|F|≤2n-4-|M|.If M is...We consider the problem of existence of a Hamiltonian cycle containing a matching and avoiding some edges in an n-cubc Qn,and obtain the following results.Let n≥3,MСE(Qn),and FСE(Qn)\M with 1≤|F|≤2n-4-|M|.If M is a matching and every vertex is incident with at least two edges in the graph Qn-F,then all edges of M lie on a Hamiltonian cycle in Qn-F.Moreover,if|M|=1 or|M|==2,then the upper bound of number of faulty edges tolerated is sharp.Our results generalize the well-known result for |M|=1.展开更多
The foundation of information society is computer interconnection network,and the key of information exchange is communication algorithm.Finding interconnection networks with simple routing algorithm and high fault-to...The foundation of information society is computer interconnection network,and the key of information exchange is communication algorithm.Finding interconnection networks with simple routing algorithm and high fault-tolerant performance is the premise of realizing various communication algorithms and protocols.Nowadays,people can build complex interconnection networks by using very large scale integration(VLSI)technology.Locally exchanged twisted cubes,denoted by(s+t+1)-dimensional LeTQ_(s,t) which combines the merits of the exchanged hypercube and the locally twisted cube.It has been proved that the LeTQ_(s,t) has many excellent properties for interconnection networks,such as fewer edges,lower overhead and smaller diameter.Embeddability is an important indicator to measure the performance of interconnection networks.We mainly study the fault tolerant Hamiltonian properties of a faulty locally exchanged twisted cube,LeTQ_(s,t)-(f_(v)+f_(e)),with faulty vertices f_(v) and faulty edges fe.Firstly,we prove that an LeTQ_(s,t) can tolerate up to s-1 faulty vertices and edges when embedding a Hamiltonian cycle,for s≥2,t≥3,and s≤t.Furthermore,we also prove another result that there is a Hamiltonian path between any two distinct fault-free vertices in a faulty LeTQ_(s,t) with up to(s-2)faulty vertices and edges.That is,we show that LeTQ_(s,t) is(s-1)-Hamiltonian and(s-2)-Hamiltonian-connected.The results are proved to be optimal in this paper with at most(s-1)-fault-tolerant Hamiltonicity and(s-2)fault-tolerant Hamiltonian connectivity of LeTQ_(s,t).展开更多
文摘Some useful layered cross product decompositons are derived both for general bit permutation networks and for(2n-1)-stage multistage interconnection networks.Several issues in related works are clarified and the rearrangeability of some interesting networks are considered.In particular, the rearrangeability of one class of networks is formulated as a new type of combinatorial design problmes.
基金supported by National Natural Science Foundation of China (No.62362005)。
文摘The reliability of a network is an important indicator for maintaining communication and ensuring its stable operation. Therefore, the assessment of reliability in underlying interconnection networks has become an increasingly important research issue. However, at present, the reliability assessment of many interconnected networks is not yet accurate,which inevitably weakens their fault tolerance and diagnostic capabilities. To improve network reliability,researchers have proposed various methods and strategies for precise assessment. This paper introduces a novel family of interconnection networks called general matching composed networks(gMCNs), which is based on the common characteristics of network topology structure. After analyzing the topological properties of gMCNs, we establish a relationship between super connectivity and conditional diagnosability of gMCNs. Furthermore, we assess the reliability of g MCNs, and determine the conditional diagnosability of many interconnection networks.
文摘Recent architectures of multi-core systems may have a relatively large number of cores that typically ranges from tens to hundreds;therefore called many-core systems.Such systems require an efficient interconnection network that tries to address two major problems.First,the overhead of power and area cost and its effect on scalability.Second,high access latency is caused by multiple cores’simultaneous accesses of the same shared module.This paper presents an interconnection scheme called N-conjugate Shuffle Clusters(NCSC)based on multi-core multicluster architecture to reduce the overhead of the just mentioned problems.NCSC eliminated the need for router devices and their complexity and hence reduced the power and area costs.It also resigned and distributed the shared caches across the interconnection network to increase the ability for simultaneous access and hence reduce the access latency.For intra-cluster communication,Multi-port Content Addressable Memory(MPCAM)is used.The experimental results using four clusters and four cores each indicated that the average access latency for a write process is 1.14785±0.04532 ns which is nearly equal to the latency of a write operation in MPCAM.Moreover,it was demonstrated that the average read latency within a cluster is 1.26226±0.090591 ns and around 1.92738±0.139588 ns for read access between cores from different clusters.
基金supported by Beijing Advanced Innovation Center for Materials Genome Engineering,Beijing Information Science and Technology University。
文摘In order to extend the application scope of NDN and realize the transmission of different NDNs across IP networks,a method for interconnecting NDN networks distributed in different areas with IP networks is proposed.Firstly,the NDN data resource is located by means of the DNS mechanism,and the gateway IP address of the NDN network where the data resource is located is found.Then,the transmission between different NDNs across the IP network is implemented based on the tunnel technology.In addition,in order to achieve efficient and fast NDN data forwarding,we have added a small number of NDN service nodes in the IP network,and proposed an adaptive probabilistic forwarding strategy and a link cost function-based forwarding strategy to make NDN data obtaining the cache service provided by the NDN service node as much as possible.The results of analysis and simulation experiments show that,the interconnectionmethod of NDN across IP network proposed is generally effective and feasible,and the link cost function forwarding strategy is better than the adaptive probability forwarding strategy.
文摘Connectivity is a vital metric to explore fault tolerance and reliability of network structure based on a graph model. Let be a connected graph. A connected graph G is called supper-κ (resp. supper-λ) if every minimum vertex cut (edge cut) of G is the set of neighbors of some vertex in G. The g-component connectivity of a graph G, denoted by , is the minimum number of vertices whose removal from G results in a disconnected graph with at least g components or a graph with fewer than g vertices. The g-component edge connectivity can be defined similarly. In this paper, we determine the g-component (edge) connectivity of varietal hypercube for small g.
基金Supported by the National Natural Science Foundation of China(61103083,61133007)National High Technology Research and Development Program of China(863Program)(2012AA01A301,2015AA01A301)
文摘Most of users are accustomed to utilizing virtual address in their parallel programs running at the scalable high-performance parallel computing systems.Therefore a virtual and physical address translation mechanism is necessary and crucial to bridge the hardware interface and software application.In this paper,a new virtual and physical translation mechanism is proposed,which includes an address validity checker,an address translation cache(ATC),a complete refresh scheme and many reliability designs.The ATC employs a large capacity embedded dynamic random access memory(eDRAM)to meet the high hit ratio requirement.It also can switch the cache and buffer mode to avoid the high latency of accessing the main memory outside.Many tests have been conducted on the real chip,which implements the address translation mechanism.The results show that the ATC has a high hit ratio while running the well-known benchmarks,and additionally demonstrates that the new high-performance mechanism is well designed.
基金the Deanship of Scientific Research at King Khalid University for funding this work through the General Research Project under Grant Number(RGP2/230/44).
文摘Unchecked breast cell growth is one of the leading causes of death in women globally and is the cause of breast cancer.The only method to avoid breast cancer-related deaths is through early detection and treatment.The proper classification of malignancies is one of the most significant challenges in the medical industry.Due to their high precision and accuracy,machine learning techniques are extensively employed for identifying and classifying various forms of cancer.Several data mining algorithms were studied and implemented by the author of this review and compared them to the present parameters and accuracy of various algorithms for breast cancer diagnosis such that clinicians might use them to accurately detect cancer cells early on.This article introduces several techniques,including support vector machine(SVM),K star(K∗)classifier,Additive Regression(AR),Back Propagation Neural Network(BP),and Bagging.These algorithms are trained using a set of data that contains tumor parameters from breast cancer patients.Comparing the results,the author found that Support Vector Machine and Bagging had the highest precision and accuracy,respectively.Also,assess the number of studies that provide machine learning techniques for breast cancer detection.
文摘Diagnosability of a multiprocessor system is one important study topic. In 2012, Peng et al. proposed a measure for fault tolerance of the system, which is called the g-good-neighbor diagnosability that restrains every fault-free node containing at least g fault-free neighbors. In 2015, Zhang et al. proposed a measure for fault diagnosis of the system, namely, g-extra diagnosability, which restrains that every fault-free component has at least g+1 fault-free nodes. In this paper, we obtain some properties of the g-good-neighbor (g-extra) diagnosability of the system and give the g-good-neighbor (g-extra) diagnosability of some graphs under the PMC model and MM<sup>*</sup> model.
基金Supported by National Natural Science Foundation of China(Grant No.61772010)。
文摘Diagnosability of multiprocessor systems is an important research topic.The system and an interconnection network have an underlying topology,which is usually presented by a graph.In 2012,Peng et al.proposed a metric for fault diagnosis of the graph,namely,the n-neighbor diagnosability that restrains every fault-free node to contain at least n fault-free neighbors.It is difficult to get the n-neighbor diagnosability of the graph from the definition of the n-neighbor diagnosability.Afterwards,some sufficient and necessary conditions are given.It is also difficult to find the n-neighbor diagnosability of the graph from those results.In this paper,we show some new sufficient conditions for the graph to be n-neighbor d-diagnosable under the MM*model.It improves the corresponding result of[Theoretical Computer Science 773(2019)107-114].
基金supported by the National Natural Science Foundation of China(61370001,U1304601)
文摘Diagnosability of a multiprocessor system is one important study topic.Cayley graph network Cay(T_n,S_n) generated by transposition trees Tnis one of the attractive underlying topologies for the multiprocessor system.In this paper,it is proved that diagnosability of Cay(T_n,S_n) is n-1 under the comparison diagnosis model for n ≥ 4.
基金supported by the National Science Foundation of USA(Grant No.9810692)University of Missouri-Kansas City Faculty Research Grant(UMKC FRG)(No.K-2-11678).
文摘It has long been an outstanding conjecture that any(2^(n)×2^(n))-stage shuffle exchange network(Omega net-work)is rearrangeable for 2n 62n.Many researchers have failed to prove this conjecture,including a recent one established by Hasan.However,nobody has pointed out its fallacy.Therefore,as one of the objectives,this paper shall clarify this fact.Since the case of n 53 has been proven by many researchers[1,2],this paper uses a con-structive approach to prove that when n 54,the 7-stage 16616 shuffle exchange network is also rearrangeable.The paper also presents the model of a balanced tree to avoid internal conflict,the representation of permutations using a connection graph and loop graph,and the con-cepts of symmetry graph and identical transform.Based on graphic composition and bipartition,the permutations 16×16 are divided into five classes,with five assignment algorithms proposed.These algorithms are simpler,clearer and easier to program.The techniques used for n=4 may provide hints for the general case of n>4.
基金financially supported by the National Natural Science Foundation of China(Nos.51922008,52072114 and 51872075)the 111 Project(No.D17007)+1 种基金Henan Center for Outstanding Overseas Scientists(No.GZS2022017)Xinxiang Major Science and Technology Projects(No.21ZD001)。
文摘The accessibility and mass transfer between catalytic sites and substrates/intermediates are essential to a catalyst's overall performance in oxygen electrocatalysis based energy devices.Here,we present an“in-situ self-sacrifice template etching strategy”for reconstructing MOF-derived M-N-C catalysts,which introduces micro-meso-macro pores with continuous apertures in a wide range and a central hollowout structure to optimize the electrochemical oxygen redox kinetics.It is realized via one-step pyrolysis of ZIF-8 single crystal epitaxially coating on a multi-functional template of the Fe,Co co-loaded mesoporous ZnO sphere.The ZnO core is reduced during the general pyrolysis of ZIF-8 into M-N-C and acts as a pore former to etch the surrounding ZIF-8 shell into diverse channels anchoring highly exposed Fe and Co-based active sites with edge enrichment.The redesigned catalyst reveals apparent structural benefits towards enhanced oxygen redox kinetics as bifunctional cathode catalysts of rechargeable zinc-air battery compared with the primitive bulk M-N-C catalysts and the mixture of commercial Pt/C and Ir/C.The unique structure-based activity advantages,the omitted template removal step and good template compatibility during synthesis make the strategy universal for the channel engineering of electrocatalysts.
基金The work was supported by the National Natural Science Foundation of China(Grant No.11401290).
文摘We consider the problem of existence of a Hamiltonian cycle containing a matching and avoiding some edges in an n-cubc Qn,and obtain the following results.Let n≥3,MСE(Qn),and FСE(Qn)\M with 1≤|F|≤2n-4-|M|.If M is a matching and every vertex is incident with at least two edges in the graph Qn-F,then all edges of M lie on a Hamiltonian cycle in Qn-F.Moreover,if|M|=1 or|M|==2,then the upper bound of number of faulty edges tolerated is sharp.Our results generalize the well-known result for |M|=1.
基金supported by the National Natural Science Foundation of China(Grant Nos.U1905211,61872196,61902195 and 61972272)Natural Science Foundation of Jiangsu Province(BK20200753)Natural Science Fund for Colleges and Universities in Jiangsu Province(General Program,19KJB520045),NUPTSF(NY219151,NY219131)。
文摘The foundation of information society is computer interconnection network,and the key of information exchange is communication algorithm.Finding interconnection networks with simple routing algorithm and high fault-tolerant performance is the premise of realizing various communication algorithms and protocols.Nowadays,people can build complex interconnection networks by using very large scale integration(VLSI)technology.Locally exchanged twisted cubes,denoted by(s+t+1)-dimensional LeTQ_(s,t) which combines the merits of the exchanged hypercube and the locally twisted cube.It has been proved that the LeTQ_(s,t) has many excellent properties for interconnection networks,such as fewer edges,lower overhead and smaller diameter.Embeddability is an important indicator to measure the performance of interconnection networks.We mainly study the fault tolerant Hamiltonian properties of a faulty locally exchanged twisted cube,LeTQ_(s,t)-(f_(v)+f_(e)),with faulty vertices f_(v) and faulty edges fe.Firstly,we prove that an LeTQ_(s,t) can tolerate up to s-1 faulty vertices and edges when embedding a Hamiltonian cycle,for s≥2,t≥3,and s≤t.Furthermore,we also prove another result that there is a Hamiltonian path between any two distinct fault-free vertices in a faulty LeTQ_(s,t) with up to(s-2)faulty vertices and edges.That is,we show that LeTQ_(s,t) is(s-1)-Hamiltonian and(s-2)-Hamiltonian-connected.The results are proved to be optimal in this paper with at most(s-1)-fault-tolerant Hamiltonicity and(s-2)fault-tolerant Hamiltonian connectivity of LeTQ_(s,t).
