Results on Relatively Prime Domination Number of Vertex Switching of Some Graphs

A Jancy Vini, C Jayasekaran


If a set S ⊆ V has at least two members and every pair of vertices u and v is such that (d(u), d(v)) = 1, then it is said to be a relatively prime dominating set. The relatively prime domination number, represented by γrpd(G), is the lowest cardinality of a relatively prime dominating set. The switching of a finite undirected graph by a subset is defined as the graph Gσ(V, E′), which is obtained from G by removing all edges between σ and its complement V − σ and adding as edges all non-edges between σ and V − σ. In this paper, we com-
pute the relatively prime domination number of vertex switching of cycle type graphs like David Star Graph, Helm Graph, Friendship Graph and Book Graph.


Dominating set, Relatively prime dominating set, Relatively prime domination number, Vertex switching

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