<?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-2385</article-id>
      <title-group>
        <article-title>Triple connected certified domination number of triangular grid with boundaries</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Kaviya</surname>
            <given-names>S.</given-names>
          </name>
          <aff>Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram, Tamil Nadu, 624302, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Mahadevan</surname>
            <given-names>G.</given-names>
          </name>
          <aff>Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram, Tamil Nadu, 624302, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Sivagnanam</surname>
            <given-names>C.</given-names>
          </name>
          <aff>Department of Mathematics and Computing Skills, University of Technology and Applied Sciences, Sur, Sultanate of Oman</aff>
        </contrib>
      </contrib-group>
      <volume>29</volume>
      <issue>7</issue>
      <fpage>2773</fpage>
      <lpage>2786</lpage>
      <pub-date date-type="pub">
        <day>21</day>
        <month>07</month>
        <year>2026</year>
      </pub-date>
      <abstract>
        <p>A dominating set S in a graph G is termed a Triple Connected Certified Dominating Set (TCCD-set) if, for each vertex v in S, either the number of neighbors of v in V – S is zero or k where k ≥ 2, and any three vertices of S are positioned on a path within the subgraph induced by S. The minimum size of a TCCD-set is known as the Triple connected certified domination Number (TCCD-number) and is symbolized as γTCC (G). This study explores the TCCD number for triangular grid of rectangular and square border.</p>
      </abstract>
      <kwd-group>
        <kwd>Triple connected</kwd>
        <kwd>Triple connected certified domination number</kwd>
        <kwd>Certified domination</kwd>
        <kwd>Triangular grid</kwd>
        <kwd>Boundaries</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>
