Some New Results on Total Equitable Domination in Graphs

Abstract

A dominating set D is total if every vertex of V is adjacent to at least one vertex of D while D is called equitable if for every u in D there exists a vertex v in V D such that |d(u)d(v)| ≤ 1. A dominating set which is both total and equitable is called total equitable dominating set The total equitable domination number of G is the minimum cardinality of a total equitable dominating set of G which is denoted by γ e t (G). In this paper we contribute some general results on this concept.