Hamiltonian性与邻域交

HAMILTONIAN PROPERTIES IN GRAPHS AND NEIGHBORHOOD UNIONS

本文考虑图G的两个不相邻点的度及邻域交、得到如下结果:图G是2—连通简单图,独立数为口,最小度δ>n—2a+2,如果对于G的任意两个不相邻点u,v如下条件之一成立 d(u)+d(v)≥n |N(u)∩N(v)|≥α-1 则G是Hamiltonian。

In this paper, by examining the bounds on |N(u)∩N(v)|, for u, v∈V(G) and uv(?)E(G), it shows that if G is a 2—reconnected graph of order n and independence number α with δ≥ n—2a+2, and d(u)+d(v)≥n or |N(u)∩N(v)|≥a—1 for every pair of non-adjacent vertices u, v, we characteris the graph is Hamiltonian.