IJPAM: Volume 120, No. 4 (2018)
COLORFUL DOMINATION , V. Swaminathan, P. Aristotle
Sri Chandrasekharendra Saraswathi Viswa Mahavidyalaya
Kanchipuram, 631 561, Tamilnadu, INDIA
Department of Mathematics
Rajalakshmi Engineering College
Chennai, 602 105, Tamilnadu, INDIA
Ramanujan Research Center in Mathematics
Saraswathi Narayanan College
Madurai, 625 022, Tamilnadu, INDIA
PG & Research Department of Mathematics
Raja Doraisingam Government Arts College
Sivagangai, 630 561, Tamilnadu, INDIA
be a finite, simple and undirected graph. A partition of into independent sets such that each independent set is dominated by a vertex belonging to is called a color class domination partition (in short -partition) [, , , , ]. The minimum cardinality of a -partition is called the -chromatic number of and is denoted by . A proper coloring of in which each vertex of the graph dominates some color class is called a dominator coloring of and the minimum number of color classes in a dominator coloring of is called the dominator chromatic number of and is denoted by [, ,, ]. In a -partition of , any set formed by selecting one vertex each from every color class becomes a dominating set of . That is, in such a dominating set each vertex has distinct color and no color is represented by more than one element. Thus, a -coloring gives rise to a dominating set which can be rightly called a colorful dominating set of (also called gamma coloring of ). In the case of -partition, this does not happen generally. So, it is a nice problem to find the minimum cardinality of a -partition which will give rise to a colorful dominating set. This new parameter is denoted by . A study of this parameter is initiated in this paper.
Received: June 7, 2017
Revised: September 9, 2017
Published: August 4, 2019
AMS Subject Classification: 05C69
Key Words and Phrases: color class domination partition, dominator chromatic number, colorful dominating set, dominator coloring
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 623 - 638