A characterization of (γt, 2γ)-block graphs

Abstract

Let γ(G) and γt(G) denote the domination number and the total domination number of a simple graph G, respectively. A (γt, 2γ)-graph is a graph with γt(G) = 2γ(G). A graph G is called a block graph if each block of G is complete. In this note, motivated by the work of Henning [Trees with large total domination number, Util. Math. 60 (2001)], we give a characterization of (γt, 2γ)-block graphs.