Discussiones Mathematicae Graph Theory (Nov 2021)
Hereditary Equality of Domination and Exponential Domination in Subcubic Graphs
Abstract
Let γ(G) and γe(G) denote the domination number and exponential domination number of graph G, respectively. Henning et al., in [Hereditary equality of domination and exponential domination, Discuss. Math. Graph Theory 38 (2018) 275–285] gave a conjecture: There is a finite set ℱ of graphs such that a graph γG satisfies (H) = γe(H) for every induced subgraph H of G if and only if G is ℱ-free. In this paper, we study the conjecture for subcubic graphs. We characterize the class ℱ by minimal forbidden induced subgraphs and prove that the conjecture holds for subcubic graphs.
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