<?xml version="1.0" encoding="UTF-8"?>
<article article-type="Research Article">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher">journal-of-information-and-optimization-sciences</journal-id>
      <journal-title-group>
        <journal-title>Journal of Information and Optimization Sciences</journal-title>
      </journal-title-group>
      <issn publication-format="electronic">2169-0103</issn>
      <issn publication-format="print">0252-2667</issn>
      <publisher>
        <publisher-name>Taru Publications</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.47974/JIOS-1586</article-id>
      <title-group>
        <article-title>Edge reflexive irregularity strength of mk -graph of path graph </article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Asif</surname>
            <given-names>Muhammad Amir</given-names>
          </name>
          <aff>School of Mathematics, Minhaj University, Lahore, 54000, Pakistan</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Siddiqui</surname>
            <given-names>Hafiz Muhammad Afzal</given-names>
          </name>
          <aff>Department of Mathematics, Lahore Campus, COMSATS University Islamabad, Lahore, 54000, Pakistan</aff>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Nadeem</surname>
            <given-names>Muhammad Faisal</given-names>
          </name>
          <aff>Department of Mathematics, Lahore Campus, COMSATS University Islamabad, Lahore, 54000, Pakistan</aff>
        </contrib>
      </contrib-group>
      <volume>47</volume>
      <issue>1</issue>
      <fpage>235</fpage>
      <lpage>250</lpage>
      <pub-date date-type="pub">
        <day>03</day>
        <month>02</month>
        <year>2025</year>
      </pub-date>
      <abstract>
        <p>In graph theory we define the total labeling, such that the edge labels and vertex labels are positive integers and even integers respectively and for different edges we have distinct weights, whereas the weight of an edge is the sum of labels of that edge and adjacent vertices, then labeling is referred as edge irregular reflexive total labeling. In this paper we calculated the exact values of reflexive edge irregularity strength for mk-graph of path graph mPn for k = 1 with n ≥ 3, m ≥ 4.</p>
      </abstract>
      <kwd-group>
        <kwd>Edge irregular reflexive total labeling</kwd>
        <kwd>mk-graphs</kwd>
        <kwd>Irregularity strength</kwd>
      </kwd-group>
      <custom-meta-group>
        <custom-meta>
          <meta-name>access</meta-name>
          <meta-value>open</meta-value>
        </custom-meta>
        <custom-meta>
          <meta-name>retracted</meta-name>
          <meta-value>no</meta-value>
        </custom-meta>
      </custom-meta-group>
    </article-meta>
  </front>
</article>
