On the Total Domination Number of Total Graphs

Abstract

Abstract Let G be a graph with no isolated vertex. A set D ⊆ V (G) is a total dominating set of G if every vertex of G is adjacent to at least one vertex in D. The total domination number of G, denoted by γt (G), is the minimum cardinality among all total dominating sets of G. In this paper we study the total domination number of total graphs T(G) of simple graphs G. In particular, we give some relationships that exist between γt(T(G)) and other domination parameters of G and of some well-known graph operators on G. Finally, we provide closed formulas on γt (T(G)) for some well-known families of graphs G.