Restrained geodetic domination in graphs

Title

Restrained geodetic domination in graphs

Creator

Mulloor J.J.; Sangeetha V.

Description

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.

Source

Discrete Mathematics, Algorithms and Applications, Vol-12, No. 6

Date

2020-01-01

Publisher

World Scientific

Subject

Cartesian product; corona product; domination number; Geodetic; join of graphs; restrained geodetic domination number

Coverage

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

Rights

Restricted Access

Relation

ISSN: 17938309

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.1142/S1793830920500846

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