On Potentially $C_k$-Graphic Sequences

Abstract

In this paper, we characterize the potentially $C_k$-graphic sequence for $k=3,4,5$. These characterizations imply several theorems due to P. Erdős, M. S. Jacobson, and J. Lehel [1], R. J. Gould, M. S. Jacobson, and J. Lehel [2], and C. H. Lai [5] and [6], respectively.