Relatively Prime Inverse Domination On Line Graph

C. Jayasekaran, Roshini L

Abstract


Let G be non-trivial graph. A subset D of the vertex set V (G) of a graph G is called a dominating set of G if every vertex in V − D is adjacent to a vertex in D. The minimum cardinality of a dominating set is called the domination number and is denoted by γ(G). If V −D contains a dominating set S of G, then S is called an inverse dominating set with respect to D. In an inverse dominating set S, every pair of vertices u and v in S such that (degu, degv) = 1, then S is called relatively prime inverse dominating set. The minimum cardinality of a relatively prime inverse dominating set is called relatively prime inverse dominating number and is denoted by γ −1 rp (G). In this paper we find relatively prime inverse dominating number of some line graphs.

Keywords


Domination, Inverse domination, Relatively prime domination.

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DOI: http://dx.doi.org/10.23755/rm.v47i0.954

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Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.