<?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-1636</article-id>
      <title-group>
        <article-title>The inclusion subsemimodule graph of a semimodule</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Alwan</surname>
            <given-names>Ahmed H.</given-names>
          </name>
          <aff>Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Nema</surname>
            <given-names>Zahraa A.</given-names>
          </name>
          <aff>Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq</aff>
        </contrib>
      </contrib-group>
      <volume>26</volume>
      <issue>6</issue>
      <fpage>1747</fpage>
      <lpage>1752</lpage>
      <pub-date date-type="pub">
        <day>01</day>
        <month>06</month>
        <year>2023</year>
      </pub-date>
      <abstract>
        <p>Let R be an abelian semiring with unity, U be an R-semimodule. The inclusion subsemimodule graph of U, indicated IS(U), is a graph with nodes that all non-trivial subsemimodules of U and two different nodes N and L are adjacent if and only if N ⊂ L or L ⊂ N. In this worke, proved that if U is subtractive semimodule then IS(U) is not connected if is a direct sum of two simple R-semimodules. Besides, it has been proved that IS(U) is a complete graph if and only if U is a uniserial semimodule. girth, diameter, chromatic and clique numbers of IS(U) have been studied. and only if U.</p>
      </abstract>
      <kwd-group>
        <kwd>Semimodule</kwd>
        <kwd>Inclusion subsemimodule graph</kwd>
        <kwd>Connectivity</kwd>
        <kwd>diameter</kwd>
        <kwd>Clique 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>
