Hereditary equality of domination and exponential domination in triangle-free Graphs

Abstract

Let 7(G) and 7e(G) denote the domination num¬ber and exponential domination number of graph G) respectively. Henning et al. [Discussiones Mathemat- icae Graph theory 38 (2018) 275-285] gave a conjecture: There is a finite set & of graphs such that some graph G satisfies 7(H) = 7e(H) for every induced subgraph H of G if and only if G is <^-free. In this paper, we study the conjecture for triangle-free graphs. We characterize the class & by minimal forbidden induced subgraphs and prove that the conjecture holds for triangle-free graphs. © 2020 Utilitas Mathematica Publishing Inc.. All rights reserved.