<?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-2346</article-id>
      <title-group>
        <article-title>The antiadjacency spectrum of some graph operations</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Farhan</surname>
            <given-names>Mohammad</given-names>
          </name>
          <aff>Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Depok, 16424, Indonesia</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>John</surname>
            <given-names>Peter</given-names>
          </name>
          <aff>Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Depok, 16424, Indonesia</aff>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Silaban</surname>
            <given-names>Denny Riama</given-names>
          </name>
          <aff>Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Depok, 16424, Indonesia</aff>
        </contrib>
      </contrib-group>
      <volume>29</volume>
      <issue>4</issue>
      <fpage>1629</fpage>
      <lpage>1650</lpage>
      <pub-date date-type="pub">
        <day>28</day>
        <month>03</month>
        <year>2026</year>
      </pub-date>
      <abstract>
        <p>Let Γ = (V, E) be a graph of order η with V = {1, 2, 3, …, η} and E ⊆ [V]2. The antiadjacency matrix of Γ is an η × η matrix where the ij-entry is 1 if ij ∉ E and 0 if otherwise. An antiadjacency matrix can be seen as the opposite of the adjacency matrix of graphs. In this paper, we give the spectrum of the antiadjacency matrix of some graph operations, namely, disjoint union of circulant graphs, Cartesian product of cycle graph and complete graph of order two, disjoint union of complete graphs, complement of a graph, and join of graphs. </p>
      </abstract>
      <kwd-group>
        <kwd>Antiadjacency matrix</kwd>
        <kwd>Spectrum</kwd>
        <kwd>Cartesian product</kwd>
        <kwd>Join</kwd>
        <kwd>Disjoint union</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>
