On Potentially \(K_k\)-graphic Sequences

Abstract

In this paper, we characterize the potentially \(K_4\)-graphic sequences. This characterization implies the value \(\sigma(K_4,n)\), which was conjectured by P. Erdős, M. S. Jacobson, and J. Lehel [1] and was confirmed by R. J. Gould, M. S. Jacobson, and J. Lehel [2] and Jiong-Sheng Li and Zixia Song [5], independently.