<?xml version="1.0" encoding="UTF-8"?>
<article article-type="Research Article">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher">journal-of-interdisciplinary-mathematics</journal-id>
      <journal-title-group>
        <journal-title>Journal of Interdisciplinary Mathematics</journal-title>
      </journal-title-group>
      <issn publication-format="electronic">2169-012X</issn>
      <issn publication-format="print">0972-0502</issn>
      <publisher>
        <publisher-name>Taru Publications</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.47974/JIM-1931</article-id>
      <title-group>
        <article-title>Modular chromatic number on inflated graphs of some tree graphs</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Sumathi</surname>
            <given-names>P.</given-names>
          </name>
          <aff>Department of Mathematics, C. Kandaswami Naidu College for Men, Anna Nagar, University of Madras, Chennai, Tamil Nadu, 600102, India</aff>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Tamilselvi</surname>
            <given-names>S.</given-names>
          </name>
          <aff>Department of Mathematics, School of Arts and Science, Vinayaka mission’s Chennai Campus, Vinayaka mission’s research foundation (Deemed to be University), Chennai, Tamil Nadu, 603104, India</aff>
        </contrib>
      </contrib-group>
      <volume>27</volume>
      <issue>5</issue>
      <fpage>1039</fpage>
      <lpage>1052</lpage>
      <pub-date date-type="pub">
        <day>30</day>
        <month>08</month>
        <year>2024</year>
      </pub-date>
      <abstract>
        <p>For any graph G(V, E), V(G) is the vertex set and E(G) is the edge set. Let the vertex coloring be called modular coloring mc (G) of G if any two adjacent vertices receive different color sums, that is, S(u) ≠ S(v) for  u, v ∈ E(G) here S(u) = ∑v ∈ N(u)C(vij). In this paper, the structural properties of an inflated tree-related graph were discussed, and in addition, the modular chromatic number for the same was determined.</p>
      </abstract>
      <kwd-group>
        <kwd>k1</kwd>
        <kwd>n - Star graph</kwd>
        <kwd>k1</kwd>
        <kwd>n</kwd>
        <kwd>n-double star graph</kwd>
        <kwd>Bm</kwd>
        <kwd>n - bi-star graph</kwd>
        <kwd>Cn - coconut tree graph</kwd>
        <kwd>Banana tree graph</kwd>
        <kwd>Perfect binary tree</kwd>
        <kwd>pn  k1</kwd>
        <kwd>m</kwd>
        <kwd>k1</kwd>
        <kwd>n  k1</kwd>
        <kwd>m</kwd>
        <kwd>Inflated graphs</kwd>
        <kwd>Modular coloring</kwd>
        <kwd>Modular chromatic 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>
