On Total Domination in some Path Related Graphs

Abstract

If G is a graph with vertex set V(G) then dominating set D subset 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 D there exists a vertex v in V(G) - D such that the degree difference between these vertices is at most one. A dominating set which is both total and equitable is called total equitable dominating set. The minimum cardinality of total dominating set of G is called total domination number of G which is denoted by gamma_t(G). The total equitable domination number of G is the minimum cardinality of total equitable domination number of G which is denoted by gamma_t^e(G). We determine the exact values of total domination number as well as total equitable domination number of some path related graphs.