完全扩容图的点圈扩张性(英文)  

Extendable cycles in the complete expansion graph

作　　者：方香[1] 阿勇嘎[1] 

机构地区：[1]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022

出　　处：《宝鸡文理学院学报（自然科学版）》2012年第1期19-22,共4页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：Supported by Natural Science Foundation of Inner Mongolia(2010MS0113);Inner mongolia normal university graduate students'research and Innovation fund(CXJJS11042)

摘　　要：目的讨论了完全扩容图的圈扩张性。阿勇嘎在2011年给出了完全扩容图的概念,完全扩容图是G□L(G)唯一的非平凡分支,其中L(G)是G的线图。方法利用归纳法对其进行讨论。结果与结论对于最小度大于2的连通且局部连通的完全扩容图,它的任一点由所在的一个6-圈经过若干次1或扩张,最后得到哈密顿圈。Aim To discuss the cycle extendibility in the complete expansion graph introduced by A Yong-ga in 2011. The complete expansion is the only non-trivial component of G□L（G）, where L（G）is the line graph of G. Methods The inductive method is adopted to discuss the aforesaid aim. Results and Conclusion For complete expansion graph of the graph which is connected, locally connected with the minimum degree larger than 2, its each vertex can be extended from a 6-cycle to a Hamiltonian cycle through a series of 1 or 2-extensions.

关 键 词：局部连通的 完全扩容图 可扩圈 

分 类 号：O157.5[理学—数学]