A Characterization On Potentially \(K_{2,5}\)-graphic Sequences

Abstract

For given a graph \(H\), agraphic sequence \(\pi = (d_1, d_2,\ldots, d_n)\) is said to be potentially \(H\)-graphic if there exists a realization of \(m\) containing \(H\) asa subgraph. Let \(K_m- H\) be the graph obtained from \(K_m\), by removing the edges set \(E(H)\) where \(H\) is a subgraph of \(K_m\). In this paper, we characterize potentially \(K_{2,5}\)-graphic sequences. This characterization implies a special case of a theorem due to Yin \(et \;al. [26]\).