文章基本信息

标题：Erdös Conjecture on Connected Residual Graphs
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作者：Liao, Jiangdong ; Long, Gonglun ; Li, Mingyong 等
期刊名称：Journal of Computers
印刷版ISSN：1796-203X
出版年度：2012
卷号：7
期号：6
页码：1497-1502
DOI：10.4304/jcp.7.6.1497-1502
语种：English
出版社：Academy Publisher
摘要：A graph G is said to be F-residual if for every point u in G, the graph obtained by removing the closed neighborhood of u from G is isomorphic to F. Similarly, if the remove of m consecutive closed neighborhoods yields Kn, then G is called m-Kn-residual graph. Erdös determine the minimum order of the m-Kn-residual graph for all m and n, the minimum order of the connected Kn-residual graph is found and all the extremal graphs are specified. Jiangdong Liao and Shihui Yang determine the minimum order of the connected 2-Kn-residual graph is found and all the extremal graphs are specified expected for n=3, and in this paper, we prove that the minimum order of the connected 3-Kn-residual graph is found and all the extremal graphs are specified expected for n=5, 7, 9,10, and we revised Erdös conjecture.
关键词：Residual-graph;Closed neighborhood; Adjacent; Cartesian product