3-Kn-Residual Graphs

Abstract

AbstractIf G is a graph such that the deletion from G of the points in each closed neighborhood results in the complete graph Kn- residual graph. 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, in [2] the minimum order of the connected Kn-residual graph is found and all the extremal graphs are specified. In [3] 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. We revised Erdös conjecture, and our method will prove Erdös conjecture for n large.KeywordsInformation EngineeringComplete GraphRegular GraphDiscrete MathematicClosed NeighborhoodThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.