Some Remarks on Degree Sets of Multigraphs

Abstract

The degree set of a graph $G$ is the set $S$ consisting of the distinct degrees of vertices in $G$. In 1977, Kapoor, Polimeni, and Wall $[2]$ determined the least number of vertices among simple graphs with a given degree set. In this note, we look at the analogue problem concerning the least order and the least size of a multigraph with a given degree set.