Paired Domination Integrity of Graphs

Title

Paired Domination Integrity of Graphs

Creator

Antony A.C.; Sangeetha V.

Description

The concept of vulnerability in a communication network plays an important role when there is a disruption in the network. There exist several graph parameters that measure the vulnerability of a communication network. Domination integrity is one of the vulnerability parameters that measure the performance of a communication network. In this paper, we introduce the concept of paired domination integrity of a graph as a new measure of graph vulnerability. Let G = (V,E) be a simple, connected graph. A set of vertices in a graph G, say S, is a paired dominating set if the following two conditions are satisfied: (i) every vertex of G has a neighbor in S and (ii) the subgraph induced by S contains a perfect matching. The paired domination integrity of G, denoted by PDI(G), is defined as PDI(G) = min{|S| + m(G - S): S is a paired dominating set of G}, where m(G - S) is the order of the largest component in the induced subgraph of G - S. In this paper, we determine few bounds relating paired domination integrity with other graph parameters and the paired domination integrity of some classes of graphs. 2024 World Scientific Publishing Company.

Source

International Journal of Foundations of Computer Science

Date

2024-01-01

Publisher

World Scientific

Subject

domination integrity; Integrity; paired dominating set; paired domination integrity

Coverage

Antony A.C., Department of Mathematics, Christ (Deemed to Be University), Bangalore, Karnataka, 560029, India; Sangeetha V., Department of Mathematics, Christ (Deemed to Be University), Bangalore, Karnataka, 560029, India

Rights

Restricted Access

Relation

ISSN: 1290541

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.1142/S0129054124500126

https://www.scopus.com/inward/record.uri?eid=2-s2.0-85197660125&doi=10.1142%2fS0129054124500126&partnerID=40&md5=bdd59b61bc89472fe23fae48d601af6f