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Asian Journal of Research in Social Sciences and Humanities
Year : 2017, Volume : 7, Issue : 3
First page : ( 544) Last page : ( 556)
Online ISSN : 2249-7315.
Article DOI : 10.5958/2249-7315.2017.00190.3

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.

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Keywords

Efficient open dominator coloring, complete graphs, complete bipartite graphs, stars, wheels, paths, cycles, gear graphs.

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