含邻域交的 Hamilton及 Hamilton连通图(英文)

Hamiltonian and Hamiltonian Connected Graphs Involving Neighborhood Intersections

对任意一对不相邻的顶点 u和 v,α( u,v)表示图 G中含 u,v的最大独立集的顶立数 .通过讨论邻域交 |N ( u)∩ N ( v) |与α( u,v)的关系 ,本文得到了关于 Hamilton及 Hamilton连通图的新的充分条件 。

For any pair of nonadjacent vertices u and v,using α(u,v) to denote the maximum cardinality of an independent vertex set of G containing both u and v.By discussing the relationship between |N(u)∩N(v)| and α(u,v), new sufficient conditions for hamiltonian and hamiltonian connected graphs are obtained.