更好的新的充分条件和hamiltonian

New Better Sufficient Condition and Hamiltonian

引入新的充分条件 ,即n阶图G的长为 2的任两点u和v及与它们均不相邻的任一点w ,|N(u)∪N(v) |+d(w )≥n ,并研究得到其hamiltonian结果为 ,若 2连通n阶图G的距离是 2的任意点u、v及与这两点均不相邻的任一点w ,|N(u)∪N(v) |+d(w )≥n ,则G是Hamilton图 .该文也得到另一个充分条件NC2

This paper introduces a new sufficient condition:Any two vertices u,v of distance 2 and another vertex w that does not adjacent to u,v in G of order n with |N(u)∪N(v)|+d(w)≥n.We consider the hamiltonian with the above condition,and the following result is obtained:if 2-connected graph G of order n satisfies any two vertices u,v of distance 2 and another vertex w that does not adjacent to u,v with |N(u)∪N(v)|+d(w)≥n,then G is Hamilton graph.The further hamiltonian result satisfying another sufficient condition NC 2 is obtained too.