ON THE SECURE EQUITABLE DOMINATION IN GRAPHS

Title

ON THE SECURE EQUITABLE DOMINATION IN GRAPHS

Creator

Annie, A.; Sangeetha, V.

Description

A secure equitable dominating set S of a graph G is a dominating set in which for any vertex v ? V (G) \ S there exists at least one vertex u ? S such that u ? Ne(v), where Ne(v) indicate the equitable neighbourhood of v, and if we swap the vertex u with v, the equitable domination property of the graph will be unharmed. ?esec(G) represents the secure equitable domination number of G, which is the cardinality of the minimum secure equitable dominating set in G. The improved bounds of the secure equitable domination number of some fundamental kinds of graphs are established in this study. Furthermore, we incorporate specific results based on the diameter, girth, and degree. Additionally, we determine the bounds of the secure equitable domination number of specific special classes of graphs. I??k University, Department of Mathematics, 2025; all rights reserved.

Source

Turkish World Mathematical Society Journal of Applied and Engineering Mathematics;Volume;15;Issue;9;pp.2156-2165

Date

01-01-2025

Publisher

Isik University

Subject

05C05; 05C69; 05C76; flower graph; helm graph; Secure equitable domination; secure equitable domination number; sunflower graph; wheel graphs,double-wheel graph

Coverage

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

Rights

Restricted Access; Hardcopy may be available in the library

Relation

ISSN: 21461147;

Format

online

Language

English

Type

Article

Identifier

https://www.scopus.com/pages/publications/105015711771?origin=resultslist