On the super domination number of graphs

Identifier:  imarina:9138942

Handle: https://hdl.handle.net/20.500.11797/imarina9138942

Authors:  Klein, Douglas J; Rodriguez-Velazquez, Juan A; Yi, Eunjeong

Abstract:
© 2020 Azarbaijan Shahid Madani University 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 define D = V (G) \ D. A set D ⊆ V (G) is called a super dominating set of G if for every vertex u ∈ D, there exists v ∈ D such that N(v) ∩ D = {u}. 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.