Efficient Open Dominator Coloring in Cycles and Paths Devi Sangeetha*,**, Shanmugapriya M. M.*** *Research Scholar, Department of Mathematics, Karpagam University, Coimbatore, India **Assistant Professor, Department of Science and Humanities, P. A. College of Engineering and Technology, Pollachi, India. sangeethadevi.a@gmail.com ***Assistant Professor, Department of Mathematics, Karpagam University, Coimbatore, India. mirdu.priya@rediffmail.com Online published on 23 March, 2017. Abstract In 2006, Gera introduced and studied the dominator chromatic number. [4]. A dominator coloring of a graph G is a proper coloring in which each vertex of G dominates all the vertices of at least one color class. The dominator chromatic number χd(G) is the minimum number of colors required for a dominator coloring of G. In this paper we introduced, a proper coloring of G is called open dominator coloring, if N(v) contains at least one color class for each v ɛ V(G). An open dominator coloring of G is called efficient open dominator coloring, if N(v) contains exactly one color class for each v ɛ V(G). An open dominator coloring of G is called efficient k-open dominator coloring, if N(v) contains exactly k color classes for each v ɛ V(G) Also, we characterized some classes of graphs which admits efficient open dominator coloring of complete graphs, complete bipartite graphs, stars, wheels, paths, cycles, gear graphs. Top Keywords Efficient open dominator coloring, complete graphs, complete bipartite graphs, stars, wheels, paths, cycles, gear graphs. Top |