Congruent dominating sets in a graph - a new concept

Abstract

A dominating set D ? V (G) is said to be a congruent dominating set of G if ?v?V (G) d(v) ? 0 ( mod ?v?D d(v) ). The minimum cardinality of a minimal congruent dominating set of G is called the congruent domination number of G which is denoted by ?cd(G). Some characterizations are established and congruent domination number for various graphs have been investigated.