<?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-1287</article-id>
      <title-group>
        <article-title>Energy and Wiener index of divisor graph of commutative ring</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Khandare</surname>
            <given-names>P. D.</given-names>
          </name>
          <aff>Department of Mathematics and Statistics, GES’s Shri Bhausaheb Vartak College, Borivali, Maharashtra, 400091, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Jogdand</surname>
            <given-names>Suryakant M</given-names>
          </name>
          <aff>Department of Mathematics, SSGM College, Loha, Nanded, Maharashtra, 431708, India</aff>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>MUNESHWAR</surname>
            <given-names>R.A.</given-names>
          </name>
          <aff>Department of Mathematics, NES’s Science College, Nanded, Maharashtra, 131602, India</aff>
        </contrib>
      </contrib-group>
      <volume>44</volume>
      <issue>5</issue>
      <fpage>957</fpage>
      <lpage>974</lpage>
      <pub-date date-type="pub">
        <day>10</day>
        <month>10</month>
        <year>2023</year>
      </pub-date>
      <abstract>
        <p>In recent paper, P. D. Khandare et al. introduced a graphical structure of non empty finite ring R called as divisor graph ⅅ[R]  and discussed some properties of the graph ⅅ[Zn]. In this article, we will continue the study of the divisor graph ⅅ[Zn]  and discuss some more properties of ⅅ[Zn].  If n ∈ N  then we derive general formula for total degree and stability number of ⅅ[Zn].  Moreover we find adjacency matrix of the graph ⅅ[Zn]  and derived formula for energy of ⅅ[Zn]  when n = pk, k ∈ N  and n = pq,  for primes p and q.</p>
      </abstract>
      <kwd-group>
        <kwd>Ring</kwd>
        <kwd>Graph</kwd>
        <kwd>Energy of graph</kwd>
        <kwd>Wiener index etc</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>
