Secure equitable domination in Cartesian product of graphs

Title

Secure equitable domination in Cartesian product of graphs

Creator

Alex, Annie; Sangeetha, V.

Description

In graphs, several domination parameters have been introduced by incorporating a combination of the existing ones. A secure equitable domination is a domination in which the dominating set admits the properties of both; secure as well as equitable dominating sets. An equitable dominating set D of a graph G is said to be secure equitable dominating set, if for every u ? V?D, there exists a vertex v ? D such that u and v are adjacent and {D?{v}}?{u} is an equitable dominating set of G. The minimum cardinality of a secure equitable dominating set of G is called the secure equitable domination number of G. In this paper, we study certain cases were the secure domination, the equitable domination and the secure equitable domination bounds are equal. Moreover, we establish the bounds of secure equitable domination number of the Cartesian product of graphs. 2025 World Scientific Publishing Company.

Source

Discrete Mathematics, Algorithms and Applications;Issue;;Article No.;2550128;

Date

01-01-2025

Publisher

World Scientific

Subject

Cartesian product; Equitable domination; secure domination; secure equitable domination

Coverage

Alex A., Department of Mathematics, CHRIST (Deemed to be University), Karnataka, Bangalore, 560029, India; Sangeetha V., Department of Mathematics, CHRIST (Deemed to be University), Karnataka, Bangalore, 560029, India

Rights

Restricted Access; Hardcopy may be available in the library

Relation

ISSN: 17938309;

Format

online

Language

English

Type

Article

Identifier

https://doi.org/10.1142/S1793830925501289

https://www.scopus.com/pages/publications/105017178132?origin=resultslist