A Characterization on Potentially \(K_6 – E(K_3)\)-graphic Sequences

Abstract

Given a graph \(H\), a graphic sequence \(\pi = (d_1, d_2, \ldots, d_n)\) is said to be potentially \(H\)-graphic if there exists a realization of \(\pi\) containing \(H\) as a subgraph.In this paper, we characterize potentially \(K_6 – E(K_3)\)-graphic sequences without zero terms, where \(K_6 – E(K_3)\) denotes the graph obtained from a complete graph on \(6\) vertices by deleting three edges forming a triangle.This characterization implies the value of \(\sigma(K_6 – E(K_3), n)\).