<?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-2268</article-id>
      <title-group>
        <article-title>Some results on the non-zero divisor graphs of Zn</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Sadiq</surname>
            <given-names>Fatema A.</given-names>
          </name>
          <aff>Department of Mathematics and Computer Applications, College of Applied Sciences, University of Technology, Baghdad, Iraq</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Ramadhan</surname>
            <given-names>Haider A.</given-names>
          </name>
          <aff>Department of Mathematics, Wasit Center, Open Educational College, Wasit, Iraq</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Aubad</surname>
            <given-names>Ali A.</given-names>
          </name>
          <aff>Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq</aff>
        </contrib>
      </contrib-group>
      <volume>28</volume>
      <issue>4-B</issue>
      <fpage>1301</fpage>
      <lpage>1307</lpage>
      <pub-date date-type="pub">
        <day>26</day>
        <month>06</month>
        <year>2025</year>
      </pub-date>
      <abstract>
        <p> In this work, we study several features of the non-zero divisor graphs (ℵZD- graph) for the ring Zn of integer modulo n. For instance, the clique number, radius, girth, domination number, and the local clustering coefficient are determined. Furthermore, we present an algorithm that calculates the clique number and draws the non-zero divisor for the ring Zn.   </p>
      </abstract>
      <kwd-group>
        <kwd>The ring Zn</kwd>
        <kwd>Non-zero divisor graphs</kwd>
        <kwd>Girth</kwd>
        <kwd>Radius</kwd>
        <kwd>Clique number</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>
