<?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-2332</article-id>
      <title-group>
        <article-title>Enhancing wireless sensor networks : A discrete mathematical model for OLEACH-based clustering and routing</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Upreti</surname>
            <given-names>Shitiz</given-names>
          </name>
          <aff>Department of Engineering and Technology, Maharishi University of Information Technology (MUIT), Lucknow, Uttar Pradesh, 226013, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Naruka</surname>
            <given-names>Mahaveer Singh</given-names>
          </name>
          <aff>Department of Engineering and Technology, Maharishi University of Information Technology (MUIT), Lucknow, Uttar Pradesh, 226013, India</aff>
        </contrib>
      </contrib-group>
      <volume>28</volume>
      <issue>6</issue>
      <fpage>2469</fpage>
      <lpage>2476</lpage>
      <pub-date date-type="pub">
        <day>09</day>
        <month>07</month>
        <year>2025</year>
      </pub-date>
      <abstract>
        <p>This paper suggests a comprehensive description of some cluster head protocols, optimization techniques, and metaheuristic-based approaches for efficient energy operation in WSNs. A mathematical framework for cluster head selection, multi-hop transmission, and network topology is suggested for optimization by machine learning, game theory, and deep learning models such as Multi-Criteria Decision-Making (MCDM) and Butterfly Ant Colony Optimization (BOA-ACO). Moreover, an optimized LEACH protocol (OLEACH) is presented with improvements cluster formation and transmission techniques to improve network lifetime and load balancing. According to simulation results, OLEACH outperforms the conventional protocols MR-LEACH, BPDA, CNNDA, and FDEAM by greatly increasing throughput by 33.3%, network lifetime by 60%, and packet delivery rate by 98%.  Through the best cluster head selection, OLEACH also minimizes long-distance transmissions, increases routing efficiency, and lowers energy usage by 42.16%. This work demonstrates the assurance of intelligent routing and clustering methods to ensure the best WSN performance, scalability, resilience, and sustainability for future applications of IoT.</p>
      </abstract>
      <kwd-group>
        <kwd>OLEACH protocol</kwd>
        <kwd>Wireless sensor networks (WSNs)</kwd>
        <kwd>Clustering</kwd>
        <kwd>Cooperative communication</kwd>
        <kwd>Discrete mathematics</kwd>
        <kwd>Energy efficiency</kwd>
        <kwd>Multi-hop routing</kwd>
        <kwd>Graph theory</kwd>
        <kwd>Network lifetime</kwd>
        <kwd>Optimization techniques</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>
