On Potentially \(K_5\) — \(E_3\)-graphic Sequences

Abstract

Let \(K_{m} – H\) be the graph obtained from \(K_{m}\) by removing the edges set \(E(H)\) of \(H\) where \(H\) is a subgraph of \(K_{m}\). In this paper, we characterize the potentially \(K_{5} – P_{3}\), \(K_{5} – A_{3}\), \(K_{5} – K_{3}\) and \(K_{5} – K_{1,3}\)-graphic sequences where \(A_{3}\) is \(P_{2}\cup K_{2}\). Moreover, we also characterize the potentially \(K_{5} – 2K_{2}\)-graphic sequences where \(pK_2\) is the matching consisted of \(p\) edges.