Edge Irregular Reflexive Labeling of Some Families of Ladder Graphs

Mohammed Ali Alghamdi\(^a\), Dina Abuzaid\(^a\), Ali Ahmad\(^b\), Muhammad Faisal Nadeem\(^{c,∗}\)

\(^a\)Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia.
\(^b\)Department of Computer Science, College of Engineering and Computer Science, Jazan University, Jazan, Saudi Arabia.
\(^c\)Department of Mathematics, COMSATS University Islamabad, Lahore Campus, 54000, Lahore, Pakistan.

Correspondence should be addressed to: smamalgamdi@kau.edu., dabuzaid@kau.edu.sa, ahmadsms@gmail.com, mfaisalnadeem@ymail.com

Copyright © 2024 Mohammed Ali Alghamdi, Dina Abuzaid, Ali Ahmad, Muhammad Faisal Nadeem. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: Received: 16 October 2024; Accepted: 16 November 2024; Published Online: 20 November 2024

Abstract

The aim of this paper is to investigate reflexive edge strength in graph theory, defined as the specialized area of an edge that is irregularly labeled, where both vertices and edges are labeled. The reflexive edge strength, res(G), is the minimal value of k for which the sum of weights of any two different edges in agraph is distinct. In this paper, reflexive edge strength of b-subdivided ladder graphs and the triangular ladder graph studied.

Keywords:

Edge irregular reflexive labeling, reflexive edge strength; ladder graph, sub-divided graphs.