J. Cyman, M.A. Henning, J. Topp
On accurate domination in graphs
Discussiones Mathematicae Graph Theory
Received 13.10.2017, Revised 29.09.2018, Accepted 17.10.2018, doi: 10.7151/dmgt.2182
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 γ\rm a(G), is the cardinality of a smallest set D that is a dominating set of G and no |D|-element subset of VG \setminus 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 γ\rm a(G) = γ(G) are characterized. Furthermore, we compare the accurate domination number with the domination number of different coronas of a graph.
domination number, accurate domination number, tree, corona.