2022/04/22 by Ghanbari, Nima · 1 citation
#05C69 #05C76 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2204.10666
Let G=(V,E) be a simple graph. A dominating set of G is a subset S⊆ V such that every vertex not in S is adjacent to at least one vertex in S. The cardinality of a smallest dominating set of G, denoted by γ(G), is the domination number of G. A dominating set S is called a super dominating set of G, if for every vertex u∈ S=V-S, there exists v∈ S such that N(v)∩ S=\u\. The cardinality of a smallest super dominating set of G, denoted by γsp(G), is the super domination number of G. In this paper, we study super domination number of some graph classes and present sharp bounds for some graph operations.