On total domination in some path related graphs

Abstract

If G is a graph with vertex set V (G) then dominating set D⊆ V (G) is called total if every vertex of V (G) is adjacent to at least one vertex of D while it is called equitable if for every vertex u in V (G)− D there exists a vertex v in D such that the degree difference between these vertices is at most one and uv is an edge in G. A dominating set which is both total and equitable is called total equitable dominating set. The minimum cardinality of a total dominating set of G is called the total domination number of G which is denoted by γt (G). The total equitable domination number of G is the minimum cardinality of total equitable dominating set of G and is denoted by γe t (G). We determine the exact values of total domination number as well as total equitable domination number of some path related graphs.