图的度和与扩圈
Extending Cycles and Degree Sums in Graphs
DOI: 10.12677/pm.2011.12014, PDF, HTML,    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

参考文献

[1] J. A. Bondy，U. S. R. Murty. Graph theory with applications. New York: Macmillan London and Elsevier, 1976.
[2] Ｇ.Ａ. Dirac. Some theorems on abstract graphs. Proceedings London Mathematical Society, 1952, s3-2(1): 69-81.
[3] O. Ore. Note on Hamilton circuits. The American Mathematical Monthly, 1960, 67: 55.
[4] G. R. T. Hendry. Extending cycles in graphs. Discrete Mathematics, 1990, 85(1): 59-72.

为你推荐