图的度和与扩圈

Extending Cycles and Degree Sums in Graphs

摘要: 本文讨论了两顶点的度和与圈可扩之间的关系，得到了如下结果：设图G的阶 ，如果G中任意一对不相邻的顶点u,v满足 ，则G中任意一个满足 的圈C是可扩的。这里圈C的下界是最好可能的。由此进一步得到，如果G中任意一对不相邻的顶点u,v满足 ，则G是完全圈可扩的。

Abstract: In this paper, we study the relations between degree sums and extending cycles in graphs. The following results is proved. Let G be a graph of order . If for each pair of nonadjacent vertices u,v in , then every cycle C of G with is extendable. By the result,we have that if for each pair of nonadjacent vertices u,v in , then G is fully cycle ex-tendable.