Restrained geodetic domination in graphs
Cartesian product; corona product; domination number; Geodetic; join of graphs; restrained geodetic domination number
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. 2020 World Scientific Publishing Company.
Discrete Mathematics, Algorithms and Applications, Vol-12, No. 6
Mulloor J.J., Department of Mathematics, CHRIST (Deemed to Be University), Bengaluru, 560029, India; Sangeetha V., Department of Mathematics, CHRIST (Deemed to Be University), Bengaluru, 560029, India