• EQUIVALENCE CHROMATIC PARTITION OF A GRAPH

Abstract

Let  be a simple finite undirected graph. A subset S of V is called an equivalence set if every component of the induced sub graph  is complete. An equivalence numberis the maximum cardinality of an equivalence set of G [3]. A proper coloring of a graph is a partition of V(G) into independent sets and the minimum cardinality of such a partition is called the chromatic number of G (). A partition of V into equivalence sets is called an equivalence partition of V. The minimum cardinality of an equivalence partition is called the equivalence chromatic number of G and is denoted by . In this paper, a partition of V(G) into equivalence sets is defined and results are derived.