Let G be a simple graph with n (≥5) vertices. In this paper, we prove that if G is 3 connected and satisfies that d(u,v) =2 implies max ｛d(u),d(v)｝ ≥(n+1) /2 for every pair of vertices u and...Let G be a simple graph with n (≥5) vertices. In this paper, we prove that if G is 3 connected and satisfies that d(u,v) =2 implies max ｛d(u),d(v)｝ ≥(n+1) /2 for every pair of vertices u and v in G , then for any two vertices x, y of G , there are (x,y) paths of length from 6 to n -1 in G , and there are (x,y) paths of length from 5 to n -1 in G unless G[(x )] = G[(y )]≌ K 4 or K 5 , or G [(x )], G [(y )] are complete and (x)∩(y)=.展开更多
Let Go and G1 be two graphs with the same vertices. The new graph G（G0, G1; M） is a graph with the vertex set V（0o） ∪）V（G1） and the edge set E（Go） UE（G1） UM, where M is an arbitrary perfect matching betwee...Let Go and G1 be two graphs with the same vertices. The new graph G（G0, G1; M） is a graph with the vertex set V（0o） ∪）V（G1） and the edge set E（Go） UE（G1） UM, where M is an arbitrary perfect matching between the vertices of Go and G1, i.e., a set of cross edges with one endvertex in Go and the other endvertex in G1. In this paper, we will show that if Go and G1 are f-fault q-panconnected, then for any f 〉 2, G（G0, G1; M） is （f ＋ 1）-fault （q ＋ 2）-panconnected.展开更多
文摘Let G be a simple graph with n (≥5) vertices. In this paper, we prove that if G is 3 connected and satisfies that d(u,v) =2 implies max ｛d(u),d(v)｝ ≥(n+1) /2 for every pair of vertices u and v in G , then for any two vertices x, y of G , there are (x,y) paths of length from 6 to n -1 in G , and there are (x,y) paths of length from 5 to n -1 in G unless G[(x )] = G[(y )]≌ K 4 or K 5 , or G [(x )], G [(y )] are complete and (x)∩(y)=.
基金partially supported by National Natural Science Foundation of China (Grant No. 10571105)supported by National Natural Science Foundation of China (Grant Nos. 10571105, 10671081)Scientific Research Fund of Hubei Provincial Education Department (Grant Nos. D20081005 T200901)
文摘Let Go and G1 be two graphs with the same vertices. The new graph G（G0, G1; M） is a graph with the vertex set V（0o） ∪）V（G1） and the edge set E（Go） UE（G1） UM, where M is an arbitrary perfect matching between the vertices of Go and G1, i.e., a set of cross edges with one endvertex in Go and the other endvertex in G1. In this paper, we will show that if Go and G1 are f-fault q-panconnected, then for any f 〉 2, G（G0, G1; M） is （f ＋ 1）-fault （q ＋ 2）-panconnected.
