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<article article-type="Research Article">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher">journal-of-interdisciplinary-mathematics</journal-id>
      <journal-title-group>
        <journal-title>Journal of Interdisciplinary Mathematics</journal-title>
      </journal-title-group>
      <issn publication-format="electronic">2169-012X</issn>
      <issn publication-format="print">0972-0502</issn>
      <publisher>
        <publisher-name>Taru Publications</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.47974/JIM-2161</article-id>
      <title-group>
        <article-title>Investigating topological spaces arising from commutative rings via associated zero divisor graphs : A holistic approach</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Ali</surname>
            <given-names>Nasir</given-names>
          </name>
          <aff>Department of Mathematics, Vehari Campus, COMSATS University Islamabad, Vehari, Punjab, 61100, Pakistan</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Qousini</surname>
            <given-names>Maysoon</given-names>
          </name>
          <aff>Faculty of Science and Information Technology, Al-zaytoonah University of Jordan, Amman, 11183, Jordan</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Qureshi</surname>
            <given-names>Muhammad Imran</given-names>
          </name>
          <aff>Department of Mathematics, Vehari Campus, COMSATS University Islamabad, Vehari, Punjab, 61100, 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, Punjab, 54000, Pakistan</aff>
        </contrib>
      </contrib-group>
      <volume>29</volume>
      <issue>2</issue>
      <fpage>279</fpage>
      <lpage>312</lpage>
      <pub-date date-type="pub">
        <day>28</day>
        <month>04</month>
        <year>2025</year>
      </pub-date>
      <abstract>
        <p>This research investigates the construction of topological spaces (TS) through zero divisor graphs (ZD-graphs) of finite commutative rings (FCR), denoted by Γ(R), having order at most 10. The vertices of these graphs correspond to the non-zero divisors (ZD) within the commutative ring, where an edge connects two different vertices if their product in the ring results in zero. The focus lies on generating associative zero divisor graphs for orders 3 through 10, providing a comprehensive exploration of the intricate relationships within these rings. The study aims to reveal the topological characteristics inherent in these graphs, shedding light on the structural properties of commutative rings. The methodology involves a systematic examination of ZD-graphs and the subsequent derivation of topologies, offering a fresh perspective on the connections between algebraic structures and TS. Lately, we presented some real life applications of our work. </p>
      </abstract>
      <kwd-group>
        <kwd>Commutative rings</kwd>
        <kwd>Zero divisor graphs</kwd>
        <kwd>Topological spaces</kwd>
        <kwd>Algebraic topology</kwd>
        <kwd>Graph theory</kwd>
        <kwd>Commutative algebra</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>
