• STRONG TOTAL NEAR EQUITABLE DOMINATION IN GRAPHS

Abstract

Let be a graph, let and be any vertex in . Then the out degree of with respect to  denoted by , is defined as . A subset  is called a near equitable dominating set of if for every there exists a vertex  such that  is adjacent to and . A near equitable dominating set is called a strong total near equitable dominating set (stned-set) if for every vertex there exists  such that  is adjacent to  and . The minimum cardinality of stned-set of  is called the strong total near equitable domination number of  and is denoted by . In this paper, we initiate a study of this parameter.