Geodesic
On Accurate Domination in Graphs
Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 3, pp. 615-627

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A dominating set of a graph G is a subset D ⊆ VG such that every vertex not in D is adjacent to at least one vertex in D. The cardinality of a smallest dominating set of G, denoted by γ(G), is the domination number of G. The accurate domination number of G, denoted by γa(G), is the cardinality of a smallest set D that is a dominating set of G and no |D|-element subset of VG D is a dominating set of G. We study graphs for which the accurate domination number is equal to the domination number. In particular, all trees G for which γa(G) = γ(G) are characterized. Furthermore, we compare the accurate domination number with the domination number of different coronas of a graph.
Keywords: domination number, accurate domination number, tree, corona 
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Cyman, Joanna; Henning, Michael A.; Topp, Jerzy. On Accurate Domination in Graphs. Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 3, pp. 615-627. http://geodesic.mathdoc.fr/item/DMGT_2019_39_3_a0/