Degree Equitable Chromatic Number of a Graph

Abstract

Let $G=(V,E)$ be a connected graph. A subset $S$ of $V$ is called a degree equitable set if the degrees of any two vertices in $S$ differ by at most one. The minimum order of a partition of $V$ into independent degree equitable sets is called the $degreeequitablechromaticnumber$ of $G$ and is denoted by ${\chi }_{de}(G)$. In this paper, we initiate a study of this new coloring parameter.