On reflexive irregularity strength of diamond network

Basher, M.

doi:10.47974/JDMSC-2190

Open Access Research Article

On reflexive irregularity strength of diamond network

^*M. BasherCorresponding authorm.basher@qu.edu.sa mohamed.basher@sci.suezuni.edu.egAffiliation 1Department of MathematicsCollege of ScienceQassim UniversityBuraydah, 51452, Saudi ArabiaAffiliation 2Department of Mathematics and Computer ScienceFaculty of ScienceSuez UniversitySuez, P. O. Box, 43221, Egypt0000-0003-4576-1586View full profile →

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pp. 2247–2259Vol. 28Issue 6September 2025DOI: 10.47974/JDMSC-2190 Crossmark XML

Received:: 06 Dec 2023
Published Online:: 09 Jun 2025
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-2190
Pages:: 2247–2259

Abstract

Graph labeling is one of the many ideas that arise while studying graph theory and has attracted considerable attention, it yields mathematical models that are applicable to numerous high-tech applications (data security, telecommunication networks, astronomy, various problems of coding theory, cryptography, etc.). The process of assigning names to the vertices and edges of a set of numbers (natural numbers) is known as labeling “tagging” or a graph label. Each domain has its own unique collection of vertices “nodes” and edges “links”, which are represented in the labeling. Consequently, for entire labeling, we consider the domain as a collection of nodes and links concurrently. The reflexive edge irregularity strength (res) is a form of entire labeling in which edge weights are different among all links and the weight of a link is calculated as the aggregate of its link tag and the tags of nodes that attached to this link. The links are tagged with positive integers, while in reflexive node irregularity strength (rvs) is entire labeling in which node weights are different among all nodes and the weight of a node is derived as the aggregate of its node tag and the tags of all links incidents at this node. In both res and rvs the links are marked with positive numbers while the nodes are marked with positive even numbers. Whether the tags are related with nodes or links, we must keep them to a minimum. If these taggings are present, they are referred to as the res or rvs of H and are expressed as res(H) or rvs(H) respectively. In this article, we computed the res and rvs for diamond network graphs.

Keywords

Diamond network graph Vertex irregular reflexive labeling Edge irregular reflexive labeling Reflexive edge strength Reflexive vertex strength Cryptography

Subject Classifications

05C7805C90

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