EQUIVALENCE DOMINATOR COLORING OF A GRAPH

N. Saradha; V.Swaminathan

Volume : VI, Issue : X, October - 2016

EQUIVALENCE DOMINATOR COLORING OF A GRAPH

N. Saradha, V. Swaminathan

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. The concept of equivalence set, sub chromatic number, generalized coloring and equivalence covering number were studied in [1],[2],[4],[6],[7],[10],[15] A partition is called an equivalence color class domination partition if each Vi is an equivalence set of G and for each Vi there exist ui in V(G) such that ui dominates Vi, . An equivalence dominator coloring is a partition of V(G) into equivalence classes of G such that each vertex of G dominates some equivalence classes in that partition. Since equivalence classes is a generalization of independence, equivalence dominator coloring generalizes dominator coloring [9] in the sense that every dominator color partition is an equivalence dominator partition. In this paper, the properties of equivalence dominator coloring are derived