A Rao-type characterization for a sequence to have a realization containing a split graph

Abstract

AbstractFor a given graph H, a non-increasing sequence π=(d1,d2,…,dn) of nonnegative integers is said to be potentially H-graphic if there exists a realization of π containing H as a subgraph. The split graph Kr+Ks¯ on r+s vertices is denoted by Sr,s. In this paper, we give a Rao-type characterization for π to be potentially Sr,s-graphic. A simplification of this characterization is also presented