Erdös Conjecture on Connected Residual Graphs

نویسندگان

  • Jiangdong Liao
  • Gonglun Long
  • Mingyong Li
چکیده

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.

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عنوان ژورنال:
  • JCP

دوره 7  شماره 

صفحات  -

تاریخ انتشار 2012