<?xml version="1.0" encoding="UTF-8"?>
<article article-type="Research Article">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher">journal-of-discrete-mathematical-sciences-and-cryptography</journal-id>
      <journal-title-group>
        <journal-title>Journal of Discrete Mathematical Sciences and Cryptography</journal-title>
      </journal-title-group>
      <issn publication-format="electronic">2169-0065</issn>
      <issn publication-format="print">0972-0529</issn>
      <publisher>
        <publisher-name>Taru Publications</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.47974/JDMSC-2803</article-id>
      <title-group>
        <article-title>Extensions of product cordial graph labeling using MATLAB</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Rathi</surname>
            <given-names>Varsha</given-names>
          </name>
          <aff>Department of Mathematics &amp; Data Science, Sharda School of Engineering &amp; Science, Sharda University, Greater Noida, Uttar Pradesh, 201310, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Srivastav</surname>
            <given-names>Sweta</given-names>
          </name>
          <aff>Department of Mathematics &amp; Data Science, Sharda School of Engineering &amp; Science, Sharda University, Greater Noida, Uttar Pradesh, 201310, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Gupta </surname>
            <given-names>Sangeeta</given-names>
          </name>
          <aff>Department of Mathematics &amp; Data Science, Sharda School of Engineering &amp; Science, Sharda University, Greater Noida, Uttar Pradesh, 201310, India</aff>
        </contrib>
      </contrib-group>
      <volume>29</volume>
      <issue>9-A</issue>
      <fpage>3341</fpage>
      <lpage>3352</lpage>
      <pub-date date-type="pub">
        <day>30</day>
        <month>09</month>
        <year>2026</year>
      </pub-date>
      <abstract>
        <p>Graph labeling is a widely studied area in graph theory with applications in computer science, network analysis, and algorithmic modeling. A binary vertex labeling function f : α(G) to {0, 1}, causes the labeling of an edge f : β(G) → {0, 1} as determined by f  (ty) = f(t)  f(y). If the number of vertices differs, this labeling is referred to as a product cordial labeling (respectively, edges) labeled with 0 and 1 does not exceed one. In this work, we extend the study of product cordial labeling using MATLAB programming. We construct and verify product cordial labelings for three classes of graphs: (i) number of copies of the shell graphs, (ii) the star structure of concentric n-sunlet graphs, and (iii) number of the copies of concentric n-sunlet graphs. The proposed MATLAB implementations provide an algorithmic approach to generate these graphs, assign labels, and validate the cordiality conditions. This computational perspective not only confirms theoretical results but also demonstrates the utility of MATLAB for investigating new extensions of product cordial graphs.</p>
      </abstract>
      <kwd-group>
        <kwd>MATLAB programming</kwd>
        <kwd>Graph labeling</kwd>
        <kwd>Product cordial labeling</kwd>
        <kwd>Concentric n-sunlet graph</kwd>
        <kwd>Star of concentric n-sunlet graph</kwd>
        <kwd>Shell graph</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>
