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
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)=.
