Geodesic
Hereditary Equality of Domination and Exponential Domination in Subcubic Graphs
Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 4, pp. 1067-1075

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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 G 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.
Keywords: dominating set, exponential dominating set, subcubic graphs 
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Chen, Xue-Gang; Wang, Yu-Feng; Wu, Xiao-Fei. Hereditary Equality of Domination and Exponential Domination in Subcubic Graphs. Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 4, pp. 1067-1075. http://geodesic.mathdoc.fr/item/DMGT_2021_41_4_a12/