理论数学  >> Vol. 1 No. 2 (July 2011)

图的度和与扩圈
Extending Cycles and Degree Sums in Graphs

DOI: 10.12677/pm.2011.12014, PDF, HTML, 下载: 2,914  浏览: 9,470  科研立项经费支持

作者: 王江鲁, 程建民:山东师范大学数学科学学院,济南

关键词: 顶点的度完全圈可扩图
Degree of Vertex; Extending Cycle

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.

文章引用: 王江鲁, 程建民. 图的度和与扩圈[J]. 理论数学, 2011, 1(2): 64-67. http://dx.doi.org/10.12677/pm.2011.12014