Hamilton连通性和邻域并条件

Hamilton-connected graphs with neighborhood union conditions

设 G =( V,E)为简单图 ,δ为图 G的最小度 ,1 987年 Faudree等人给出 N C=min{| N( x)∪ N ( y)‖ x,y∈ V( G) ,xy∈ N ( G) },有关文献曾研究 3连通的 H连通图 ,本文进一步得到 :若 G是 n阶 2连通图 ,且 N C≥ n -δ,则 G除几个图外均是H连通图 .从而 ,完成了邻域并条件的

Let G=(V,E) to be a simple graph, NC=min{|N(x)∪N(y)‖x,y∈V(G),xy ∈N(G)},minimum degree of G deonoted by δ. In this paper the Hamilton-connected graphs of order n with connectivity at least 2 which satisfying the condition NC≥n-δ are studied, and that if G is 2-connected graph of order n with NC≥n-δ, then G is Hamilton-connected graphs or G∈{G 2:(K s+K h),G n/2∨K c n/2,G 3:(K (n-3)/3+K (n-3)/3+K (n-3)/3)} are showed.