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On intersection graph of ideals of a near-ring in terms of its essential ideals.

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Title: On intersection graph of ideals of a near-ring in terms of its essential ideals.
Authors: Pal, Pavel (AUTHOR) ju.pavel86@gmail.com, Jana, Jyotirmoy (AUTHOR) jyotirmoyjana.1996@gmail.com
Source: Discussiones Mathematicae: General Algebra & Applications. 2025, Vol. 45 Issue 2, p387-405. 19p.
Subjects: Ideals (Algebra), Intersection graph theory, Semirings (Mathematics), Graph connectivity, Complete graphs, Graph theory
Abstract: Let N be a near-ring and I(N) denote the set of all non-trivial (i.e., non-zero proper) ideals of N. In this paper, the intersection graph of ideals of N has been introduced as a simple undirected graph denoted by G(N) whose vertex set is I(N) and two vertices I and J are adjacent if and only if I ≠ J and I ∩ J ≠ {0}. The graph G(N) has been studied mainly using the direct sum decomposition and the essential ideals of N. Here, some neces- sary and sufficient conditions for G(N) to be connected and complete have been obtained. Under some restrictions on N and G(N), some graph parameters such as chromatic number, independence number, domination number, hull number, geodetic number as well as some graphical properties of G(N) such as being chordal, star etc. have been obtained. [ABSTRACT FROM AUTHOR]
Copyright of Discussiones Mathematicae: General Algebra & Applications is the property of University of Zielona Gora and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: On intersection graph of ideals of a near-ring in terms of its essential ideals.
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  Data: <searchLink fieldCode="AR" term="%22Pal%2C+Pavel%22">Pal, Pavel</searchLink> (AUTHOR)<i> ju.pavel86@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Jana%2C+Jyotirmoy%22">Jana, Jyotirmoy</searchLink> (AUTHOR)<i> jyotirmoyjana.1996@gmail.com</i>
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  Data: <searchLink fieldCode="DE" term="%22Ideals+%28Algebra%29%22">Ideals (Algebra)</searchLink><br /><searchLink fieldCode="DE" term="%22Intersection+graph+theory%22">Intersection graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Semirings+%28Mathematics%29%22">Semirings (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+connectivity%22">Graph connectivity</searchLink><br /><searchLink fieldCode="DE" term="%22Complete+graphs%22">Complete graphs</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink>
– Name: Abstract
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  Data: Let N be a near-ring and I(N) denote the set of all non-trivial (i.e., non-zero proper) ideals of N. In this paper, the intersection graph of ideals of N has been introduced as a simple undirected graph denoted by G(N) whose vertex set is I(N) and two vertices I and J are adjacent if and only if I ≠ J and I ∩ J ≠ {0}. The graph G(N) has been studied mainly using the direct sum decomposition and the essential ideals of N. Here, some neces- sary and sufficient conditions for G(N) to be connected and complete have been obtained. Under some restrictions on N and G(N), some graph parameters such as chromatic number, independence number, domination number, hull number, geodetic number as well as some graphical properties of G(N) such as being chordal, star etc. have been obtained. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: <i>Copyright of Discussiones Mathematicae: General Algebra & Applications is the property of University of Zielona Gora and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.7151/dmgaa.1484
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        Text: English
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        PageCount: 19
        StartPage: 387
    Subjects:
      – SubjectFull: Ideals (Algebra)
        Type: general
      – SubjectFull: Intersection graph theory
        Type: general
      – SubjectFull: Semirings (Mathematics)
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      – SubjectFull: Graph connectivity
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      – SubjectFull: Complete graphs
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      – SubjectFull: Graph theory
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              M: 07
              Text: 2025
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              Y: 2025
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