Title of article :
On the super domination number of graphs
Author/Authors :
Klein, Douglas J Texas A&M University at Galveston - Foundational Sciences, P.O. Box 1675 Galveston, USA , Rodriguez-Velazquez, Juan A Universitat Rovira i Virgili - Departament d'Enginyeria Informatica i Matematiques Av. Paisos Catalans 26, 43007 Tarragona, Spain , Yi, Eunjeong Texas A&M University at Galveston - Foundational Sciences, P.O. Box 1675 Galveston, USA
Abstract :
The open neighborhood of a vertex v of a graph G is the set N(v) consisting
of all vertices adjacent to v in G. For D ⊊ V (G), we dene D = V (G) n D. A
set D ⊊ V (G) is called a super dominating set of G if for every vertex u 2 D, there
exists v 2 D such that N(v) D = fug. The super domination number of G is the
minimum cardinality among all super dominating sets of G. In this paper, we obtain
closed formulas and tight bounds for the super domination number of G in terms of
several invariants of G. We also obtain results on the super domination number of
corona product graphs and Cartesian product graphs.
Keywords :
Corona product , Cartesian product , Domination number , Super domination number
Journal title :
Communications in Combinatorics and Optimization
