## EQUITABLE AND OUTDEGREE EQUITABLE DOMINATION NUMBER OF GRAPHS

## EQUITABLE AND OUTDEGREE EQUITABLE DOMINATION NUMBER OF GRAPHS

*Thasneem T. R., M. K. Menon*

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## Abstract

Let G = (V;E) be a simple graph. A subset D of V is said to be a domi- nating set of G, if each vertex in V is either in D or has a neighbour in D. A subset D of V is said to be an equitable dominating set of G, if for every v 2 V ????D, there exists a vertex u 2 D such that uv 2 E(G) and jdeg(u)????deg(v)j 1. The minimum cardinality of an equitable dominating set of G, denoted by e(G), is called the equitable domination number of G. The edges from a vertex u 2 D to V ????D are called the dominating edges of u from D. A dominating set D is called an outdegree equitable dominating set if the di erence between the cardinalities of the sets of dominating edges from any two points of D is atmost one. The minimum cardinality of an outdegree equitable dominating set of G, denoted by oe(G) is called the outdegree equitable domination number of G. In this paper we study equitable domination number and outdegree equitable domination number of some graphs.

## Keywords

Equitable domination, Outdegree equitable domination, Equitable isolates.