• 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.
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