<?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-2394</article-id>
      <title-group>
        <article-title>Optimal embedding of extended Sierpiński networks into windmill and necklace graphs</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Joshwa</surname>
            <given-names>P. Leo</given-names>
          </name>
          <aff>Department of Mathematics, Hindustan Institute of Technology &amp; Science, Chennai, Tamil Nadu, 603103, India</aff>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Rajan</surname>
            <given-names>R. Sundara</given-names>
          </name>
          <aff>Department of Mathematics, Rajalakshmi Engineering College, Chennai, Tamil Nadu, 602105, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Rajalaxmi</surname>
            <given-names>T. M.</given-names>
          </name>
          <aff>Department of Mathematics, Sri Sivasubramaniya Nadar College of Engineering, Chennai, Tamil Nadu, 603110, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Emilet</surname>
            <given-names>D. Ahima</given-names>
          </name>
          <aff>Department of Mathematics, Hindustan Institute of Technology &amp; Science, Chennai, Tamil Nadu, 603103, India</aff>
        </contrib>
      </contrib-group>
      <volume>29</volume>
      <issue>4</issue>
      <fpage>1695</fpage>
      <lpage>1706</lpage>
      <pub-date date-type="pub">
        <day>08</day>
        <month>04</month>
        <year>2026</year>
      </pub-date>
      <abstract>
        <p>The Sierpińki network S(p, q) is a hierarchical, self-similar structure with broad applications in multiprocessor interconnection and VLSI design. In this work, we study its enhanced variant, S++ (p, q) for p ≥ 2, q ≥ 3, focusing on the problem of minimum wirelength embedding into windmill and necklace graphs. These results offer practical advances for hierarchical network layout, contributing to the design of scalable and low-latency parallel computing architectures.</p>
      </abstract>
      <kwd-group>
        <kwd>Embedding</kwd>
        <kwd>Wirelength</kwd>
        <kwd>Extended Sierpiński network S++ (p</kwd>
        <kwd>q)</kwd>
        <kwd>Windmill</kwd>
        <kwd>Necklace 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>
