<?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-2166</article-id>
      <title-group>
        <article-title>Independent 2-domination polynomials in complete bipartite graphs</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Mahmoodzadeh</surname>
            <given-names>Hamed</given-names>
          </name>
          <aff>Department of Mathematics, Faculty of Mathematics, Statistics, and Computer Science, Semnan University, Semnan, 35131-19111, Iran</aff>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Semnani</surname>
            <given-names>Saied Mohammadian</given-names>
          </name>
          <aff>Department of Mathematics, Faculty of Mathematics, Statistics, and Computer Science, Semnan University, Semnan, 35131-19111, Iran</aff>
        </contrib>
      </contrib-group>
      <fpage>1</fpage>
      <lpage>11</lpage>
      <pub-date date-type="pub">
        <day>06</day>
        <month>10</month>
        <year>2026</year>
      </pub-date>
      <abstract>
        <p>This paper investigates the independent 2-domination polynomial of complete bipartite graphs Km, n. We establish closed formulas for this polynomial and describe all independent 2-dominating sets in such graphs. The findings illustrate how the bipartite structure determines the enumeration of these sets and provide further insight into domination-type polynomials in special graph families.</p>
      </abstract>
      <kwd-group>
        <kwd>Independent 2-dominating sets</kwd>
        <kwd>Independent 2-domination number</kwd>
        <kwd>Independent 2-domination polynomial</kwd>
        <kwd>Bipartite 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>
