Degree coprime domination and degree non-coprime domination in graphs
Keywords:
degree coprime dominating set, degree non-coprime dominating set, degree coprime domination number, degree non-coprime domination numberAbstract
Let G(V,E) be a finite, undirected, simple graph without isolated vertices. A dominating set D of V(G) is called a degree coprime dominating set of G if for every v∈V-D, there exist a vertex u∈D such that uv∈E(G) and (deg u,deg v)=1. The minimum cardinality of a degree coprime dominating set is called the degree coprime domination number of G and is denoted by γ_cp (G). A dominating set D of V(G) is called a degree non-coprime dominating set of G if for every v∈V-D, there exist a vertex u∈D such that uv∈E(G) and (deg u,deg v)≠1. The minimum cardinality of a degree non-coprime dominating set is called the degree non-coprime domination number and is denoted by γ_ncp (G). We obtain the degree coprime domination number for some graphs.
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