<?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-2861</article-id>
      <title-group>
        <article-title>On product cordial labeling of helm graphs and their subdivisions : An algorithmic approach</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, Noida, Uttar Pradesh, 201310, India</aff>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <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, 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, Noida, Uttar Pradesh, 201310, India</aff>
        </contrib>
      </contrib-group>
      <volume>29</volume>
      <issue>9-A</issue>
      <fpage>3453</fpage>
      <lpage>3462</lpage>
      <pub-date date-type="pub">
        <day>30</day>
        <month>09</month>
        <year>2026</year>
      </pub-date>
      <abstract>
        <p>This paper deals with product cordial labeling in graphs, with emphasis being placed on helm graphs and their subdivisions. Let G = (V, E) be a simple graph. Given a vertex labeling function f : V (G) → {0, 1}, we define an edge labeling function f ∗ : E(G) → {0, 1} given by f ∗(uv) = f (u)f (v). Graph G is called product cordial if the difference between the number of vertices labeled 0 and 1 and the number of edges labeled 0 and 1 is at most one. An algorithmic approach for the construction and testing of product cordial labelings is introduced in this paper. Based on our approach, we obtain product cordial labeling schemes for helm graphs and their subdivisions. Moreover, we provide sufficient conditions for the existence of such labelings for both graph classes. We show that helm graphs and their subdivisions indeed possess product cordial labelings based on the given scheme.</p>
      </abstract>
      <kwd-group>
        <kwd>Product cordial labelling</kwd>
        <kwd>Helm graph</kwd>
        <kwd>Graph subdivision</kwd>
        <kwd>Algorithmic graph theory</kwd>
        <kwd>Discrete mathematics</kwd>
        <kwd>Graph labeling</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>
