# IJPAM: Volume 104, No. 2 (2015)

**EQUITABLE DOMINATING CHROMATIC SETS IN GRAPHS**

Department of Mathematics

Sethu Institute of Technology

Kariapatti, Tamilnadu, INDIA

Department of Mathematics

Mannar Thirumalai Naicker College

Madurai, Tamilnadu, INDIA

Ramanujan Research Center in Mathematics

Saraswathi Narayanan College

Madurai, Tamilnadu, INDIA

**Abstract. **Let be a simple graph. A subset of is said to be an equitable dominating set of if for every vertex there exists a vertex such that and
. A subset of is said to be an equitable dominating chromatic set of if is an equitable dominating set of and
. Since is an equitable dominating chromatic set of , the existence of equitable dominating chromatic set in a graph is guaranteed. The minimum cardinality of such a set is called the equitable dominating chromatic number of and is denoted by
. The property of equitable dominating chromatic set is super hereditary. Hence equitable dominating chromatic set is minimal if and only if it is -minimal. Characterization of minimal equitable dominating chromatic sets is derived. The values of
for many classes of graphs have been found. It is established that
. Interesting results are proved with respect to the new parameters.

**Received: **April 29, 2015

**AMS Subject Classification: **05C17, 05C69, 05C70

**Key Words and Phrases: **equitable dominating set, equitable dominating chromatic set

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**DOI: 10.12732/ijpam.v104i2.4**

International Journal of Pure and Applied Mathematics

**How to cite this paper?****Source:****ISSN printed version:**1311-8080

**ISSN on-line version:**1314-3395

**Year:**2015

**Volume:**104

**Issue:**2

**Pages:**193 - 202

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