Results on Relatively Prime Dominating Sets in Graphs
C. Jayasekaran, A. Jancy Vini · Annals of Pure and Applied Mathematics · 2017
In this paper we introduce relatively prime dominating set of a graph G. Let G be a non-trivial graph.A set S ⊆ V is said to be relatively prime dominating set if it is a dominating set with at least two elements and for every pair of vertices u and v in S such that (deg u, deg v) = 1.The minimum cardinality of a relatively prime dominating set is called relatively prime domination number and it is denoted by rpd γ (G) .If there is no such pair exist then rpd γ (G) = 0. We characterize connected unicyclic graphs with rpd γ (G)=2 and also we prove that rpd m, n γ (K ) = 2 iff (m, n) = 1 and rpd γ ( n P ) = 2 for n ≥ 4.