Sombor指标是一种离散数学图论中的拓扑指标,能够清晰地反应图的特征。讨论拓扑指标的极值问题能够分析图的基本性质。本文讨论了在完美匹配的单圈图当中,指数型Sombor指标的极值问题。其中指数型Sombor指标定义为: eSO(G) =uv∈E(G)∑e...Sombor指标是一种离散数学图论中的拓扑指标,能够清晰地反应图的特征。讨论拓扑指标的极值问题能够分析图的基本性质。本文讨论了在完美匹配的单圈图当中,指数型Sombor指标的极值问题。其中指数型Sombor指标定义为: eSO(G) =uv∈E(G)∑e√d2G(u)+d2G(v) 本文的主要结论是:若G∈U2m,m,则eSO(G) ≤ eSO(U2m,m)且eSO(U2m,m) ≤ (m - 2)e√5 + me√(m+1)2+4+e2√2+e√(m+1)2+1等号成立当且仅当G≅U2m,m,其中m为图G的匹配数。The Sombor Index is a Topological Index in Discrete Mathematical Graph Theory which can clearly reflect the characteristics of the graph. While the Extreme value of Topological Index is the key to analyse the basic properties of the graph. This paper discusses the Extreme Value of Exponential Sombor Index in Unicyclic Graph with Perfect Matching. The exponential Sombor index is defined as:eSO(G) =uv∈E(G)∑e√d2G(u)+d2G(v) The main result of this paper is:If G∈U2m,m,Then eSO(G) ≤ eSO(U2m,m),eSO(U2m,m) ≤ (m - 2)e√5 + me√(m+1)2+4+e2√2+e√(m+1)2+1If and only if G≅U2m,m the equal sign is established, Where m is the matching number of Graph G.展开更多
Any number that can be uniquely determined by a graph is called a graph invariant.During the last twenty years’countless mathematical graph invariants have been characterized and utilized for correlation analysis.How...Any number that can be uniquely determined by a graph is called a graph invariant.During the last twenty years’countless mathematical graph invariants have been characterized and utilized for correlation analysis.However,no reliable examination has been embraced to decide,how much these invariants are related with a network graph or molecular graph.In this paper,it will discuss three different variants of bridge networks with good potential of prediction in the field of computer science,mathematics,chemistry,pharmacy,informatics and biology in context with physical and chemical structures and networks,because k-banhatti sombor invariants are freshly presented and have numerous prediction qualities for different variants of bridge graphs or networks.The study solved the topology of a bridge graph/networks of three different types with two invariants KBanhatti Sombor Indices and its reduced form.These deduced results can be used for the modeling of computer networks like Local area network(LAN),Metropolitan area network(MAN),and Wide area network(WAN),backbone of internet and other networks/structures of computers,power generation,bio-informatics and chemical compounds synthesis.展开更多
Due to a tremendous increase in mobile traffic,mobile operators have started to restructure their networks to offload their traffic.Newresearch directions will lead to fundamental changes in the design of future Fifth...Due to a tremendous increase in mobile traffic,mobile operators have started to restructure their networks to offload their traffic.Newresearch directions will lead to fundamental changes in the design of future Fifthgeneration(5G)cellular networks.For the formal reason,the study solves the physical network of the mobile base station for the prediction of the best characteristics to develop an enhanced network with the help of graph theory.Any number that can be uniquely calculated by a graph is known as a graph invariant.During the last two decades,innumerable numerical graph invariants have been portrayed and used for correlation analysis.In any case,no efficient assessment has been embraced to choose,how much these invariants are connected with a network graph.This paper will talk about two unique variations of the hexagonal graph with great capability of forecasting in the field of optimized mobile base station topology in setting with physical networks.Since K-banhatti sombor invariants(KBSO)and Contrharmonic-quadratic invariants(CQIs)are newly introduced and have various expectation characteristics for various variations of hexagonal graphs or networks.As the hexagonal networks are used in mobile base stations in layered,forms called honeycomb.The review settled the topology of a hexagon of two distinct sorts with two invariants KBSO and CQIs and their reduced forms.The deduced outcomes can be utilized for the modeling of mobile cellular networks,multiprocessors interconnections,microchips,chemical compound synthesis and memory interconnection networks.The results find sharp upper bounds and lower bounds of the honeycomb network to utilize the Mobile base station network(MBSN)for the high load of traffic and minimal traffic also.展开更多
文摘Sombor指标是一种离散数学图论中的拓扑指标,能够清晰地反应图的特征。讨论拓扑指标的极值问题能够分析图的基本性质。本文讨论了在完美匹配的单圈图当中,指数型Sombor指标的极值问题。其中指数型Sombor指标定义为: eSO(G) =uv∈E(G)∑e√d2G(u)+d2G(v) 本文的主要结论是:若G∈U2m,m,则eSO(G) ≤ eSO(U2m,m)且eSO(U2m,m) ≤ (m - 2)e√5 + me√(m+1)2+4+e2√2+e√(m+1)2+1等号成立当且仅当G≅U2m,m,其中m为图G的匹配数。The Sombor Index is a Topological Index in Discrete Mathematical Graph Theory which can clearly reflect the characteristics of the graph. While the Extreme value of Topological Index is the key to analyse the basic properties of the graph. This paper discusses the Extreme Value of Exponential Sombor Index in Unicyclic Graph with Perfect Matching. The exponential Sombor index is defined as:eSO(G) =uv∈E(G)∑e√d2G(u)+d2G(v) The main result of this paper is:If G∈U2m,m,Then eSO(G) ≤ eSO(U2m,m),eSO(U2m,m) ≤ (m - 2)e√5 + me√(m+1)2+4+e2√2+e√(m+1)2+1If and only if G≅U2m,m the equal sign is established, Where m is the matching number of Graph G.
基金This project was funded by the Deanship of Scientific Research(DSR),King Abdul-Aziz University,Jeddah,Saudi Arabia under Grant No.(RG-11-611-43).
文摘Any number that can be uniquely determined by a graph is called a graph invariant.During the last twenty years’countless mathematical graph invariants have been characterized and utilized for correlation analysis.However,no reliable examination has been embraced to decide,how much these invariants are related with a network graph or molecular graph.In this paper,it will discuss three different variants of bridge networks with good potential of prediction in the field of computer science,mathematics,chemistry,pharmacy,informatics and biology in context with physical and chemical structures and networks,because k-banhatti sombor invariants are freshly presented and have numerous prediction qualities for different variants of bridge graphs or networks.The study solved the topology of a bridge graph/networks of three different types with two invariants KBanhatti Sombor Indices and its reduced form.These deduced results can be used for the modeling of computer networks like Local area network(LAN),Metropolitan area network(MAN),and Wide area network(WAN),backbone of internet and other networks/structures of computers,power generation,bio-informatics and chemical compounds synthesis.
基金funded by the Deanship of Scientific Research(DSR),King Abdul-Aziz University,Jeddah,Saudi Arabia under Grant No.(RG−11–611–43).
文摘Due to a tremendous increase in mobile traffic,mobile operators have started to restructure their networks to offload their traffic.Newresearch directions will lead to fundamental changes in the design of future Fifthgeneration(5G)cellular networks.For the formal reason,the study solves the physical network of the mobile base station for the prediction of the best characteristics to develop an enhanced network with the help of graph theory.Any number that can be uniquely calculated by a graph is known as a graph invariant.During the last two decades,innumerable numerical graph invariants have been portrayed and used for correlation analysis.In any case,no efficient assessment has been embraced to choose,how much these invariants are connected with a network graph.This paper will talk about two unique variations of the hexagonal graph with great capability of forecasting in the field of optimized mobile base station topology in setting with physical networks.Since K-banhatti sombor invariants(KBSO)and Contrharmonic-quadratic invariants(CQIs)are newly introduced and have various expectation characteristics for various variations of hexagonal graphs or networks.As the hexagonal networks are used in mobile base stations in layered,forms called honeycomb.The review settled the topology of a hexagon of two distinct sorts with two invariants KBSO and CQIs and their reduced forms.The deduced outcomes can be utilized for the modeling of mobile cellular networks,multiprocessors interconnections,microchips,chemical compound synthesis and memory interconnection networks.The results find sharp upper bounds and lower bounds of the honeycomb network to utilize the Mobile base station network(MBSN)for the high load of traffic and minimal traffic also.
