On basis of two definitions that 1. an induced subgraph by a vertex vi E G and its neighbors in G is defined a vertex adjacent closed subgraph denoted by Qi （=G[V（Nvi）]）, with the vertex vi called the hub; 2. A r...On basis of two definitions that 1. an induced subgraph by a vertex vi E G and its neighbors in G is defined a vertex adjacent closed subgraph denoted by Qi （=G[V（Nvi）]）, with the vertex vi called the hub; 2. A r（k,1）-1 vertices connected graph is called a （k,l）-Ramsey graph denoted by RG（k,l）,if and only if 1. RG（k,l） contains only cliques of degree k-1, and its complement contains only cliques of degree l-l; 2. the intersect Qi∩Qj of any two nonadjacent vertices vi and vj of RG（k,1） contains Kk.2, and the intersect Qi∩Qj of any two nonadjacent vertices vi and vj of its complement RG（l,k） contains KI.2. Two theorems that theoreml ： the biggest clique in G is contained in some Qi of G, and theorem2： r（k,l）= [ V（RG（k,I）） I ＋1 are put forward and proved in this paper. With those definitions and theorems as well as analysis of property of chords a method for quick inspection and building RG（k,I） is proposed. Accordingly, RG（10,3） and its complement are built, which are respectively the strongly 29-regular graph and the strongly 10-regular graph on orders 40. We have tested RG（10,3） and its complement RG（3,10）,and gotten r（3,10）=41.展开更多
文摘On basis of two definitions that 1. an induced subgraph by a vertex vi E G and its neighbors in G is defined a vertex adjacent closed subgraph denoted by Qi （=G[V（Nvi）]）, with the vertex vi called the hub; 2. A r（k,1）-1 vertices connected graph is called a （k,l）-Ramsey graph denoted by RG（k,l）,if and only if 1. RG（k,l） contains only cliques of degree k-1, and its complement contains only cliques of degree l-l; 2. the intersect Qi∩Qj of any two nonadjacent vertices vi and vj of RG（k,1） contains Kk.2, and the intersect Qi∩Qj of any two nonadjacent vertices vi and vj of its complement RG（l,k） contains KI.2. Two theorems that theoreml ： the biggest clique in G is contained in some Qi of G, and theorem2： r（k,l）= [ V（RG（k,I）） I ＋1 are put forward and proved in this paper. With those definitions and theorems as well as analysis of property of chords a method for quick inspection and building RG（k,I） is proposed. Accordingly, RG（10,3） and its complement are built, which are respectively the strongly 29-regular graph and the strongly 10-regular graph on orders 40. We have tested RG（10,3） and its complement RG（3,10）,and gotten r（3,10）=41.
