2021/11/23 by Ghanbari, Nima
#05C38 #05C69 #05C75 #05C76 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2111.11817
Let G=(V,E) be a simple graph. A dominating set of G is a subset D⊆ V 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. A dominating set D is called co-even dominating set if the degree of vertex v is even number for all v∈ V-D. The cardinality of a smallest co-even dominating set of G, denoted by γcoe(G), is the co-even domination number of G. In this paper, we find more results on co-even domination number of graphs and count the number of co-even dominating sets of some specific graphs.