Open Journal of Discrete Applied Mathematics
Vol. 7 (2024), Issue 2, pp. 23-34
ISSN: 2617-9687 (Online) 2617-9679 (Print)
DOI: 10.30538/psrp-odam2024.0100
On edge irregularity strength of some classes of Toeplitz graphs
Noha Mohammad Seyam\(^1,\) Muhammad Faisal Nadeem$^{2,*}$
\(^1\) College of Applied Sciences Mathematical Sciences Department, Umm Al-Qura University, Makkah Saudi Arabia; nmseyam@uqu.edu.sa
\(^2\) Department of Mathematics, COMSATS University Islamabad Lahore Campus, Lahore 54000 Pakistan; mfaisalnadeem@ymail.com
Copyright © 2024 Noha Mohammad Seyam, 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.
Received: May 14, 2024 – Accepted: June 09, 2024 – Published: June 30, 2024
Abstract
An edge irregular \(k\)-labeling of a graph \(G\) is a labeling of vertices of \(G\) with labels from the set \(\{1,2,3,\dots,k\}\) such that no two edges of \(G\) have same weight. The least value of \(k\) for which a graph \(G\) has an edge irregular \(k\)-labeling is called the edge irregularity strength of \(G\). Ahmad et. al. [1] showed the edge irregularity strength of some particular classes of Toeplitz graphs. In this paper we generalize those results and finds the exact values of the edge irregularity strength for some generalize classes of Toeplitz graphs.
Keywords:
irregular assignment; irregularity strength; edge irregularity strength; Toeplitz graph