On total domination and total equitable domination in graphs

Abstract

A dominating set D of a graph G is called total if every vertex of V (G) is adjacent to at least one vertex of D, equivalently if N(D) = V (G) then D is called total dominating set. A dominating set D is called total equitable dominating set if it is total and for every vertex in V (G) − D there exists a vertex in D such that they are adjacent and difference between their degrees is at most one. The minimum cardinality of a total (total equitable) dominating set is called total (total equitable) domination number of G which is denoted by γt (G)(γe t (G)). We have investigated exact value of these parameters for some graphs.