Research PaperNo Access

Restrained geodetic domination in graphs

John Joy Mulloor

https://orcid.org/0000-0003-2370-8602

Department of Mathematics, CHRIST (Deemed to be University), Bengaluru 560029, India

E-mail Address: john.joy@res.christuniversity.in

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and

V. Sangeetha

Department of Mathematics, CHRIST (Deemed to be University), Bengaluru 560029, India

E-mail Address: sangeetha.shathish@christuniversity.in

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https://doi.org/10.1142/S1793830920500846Cited by:5 (Source: Crossref)

Abstract

Let $G = (V, E)$ be a graph with edge set $E$ and vertex set $V$ . For a connected graph $G$ , a vertex set $S$ of $G$ is said to be a geodetic set if every vertex in $G$ lies in a shortest path between any pair of vertices in $S$ . If the geodetic set $S$ is dominating, then $S$ is geodetic dominating set. A vertex set $S$ of $G$ is said to be a restrained geodetic dominating set if $S$ is geodetic, dominating and the subgraph induced by $V - S$ has no isolated vertex. The minimum cardinality of such set is called restrained geodetic domination (rgd) number. In this paper, rgd number of certain classes of graphs and 2-self-centered graphs was discussed. The restrained geodetic domination is discussed in graph operations such as Cartesian product and join of graphs. Restrained geodetic domination in corona product between a general connected graph and some classes of graphs is also discussed in this paper.

Keywords:

AMSC: 05C69

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