TARU PUBLICATIONS
Journal of Discrete Mathematical Sciences and Cryptography cover

Journal of Discrete Mathematical Sciences and Cryptography

(Since 1998)
Hybrid ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

CiteScore 2025: 2.7 (Q1)

Powered by:Powered by

Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Taru Online First Current IssueSpecial IssuesBrowse all Issues
Journal of Discrete Mathematical Sciences and Cryptography
Open Access Research Article

The inclusion subsemimodule graph of a semimodule

* ,

* Corresponding author · click or hover a name for details

pp. 1747–1752Vol. 26Issue 6September 2023DOI: 10.47974/JDMSC-1636 Crossmark XML
Received:
05 May 2022
Accepted:
05 Jun 2022
Published Online:
01 Jun 2023
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-1636
Pages:
1747–1752

Abstract

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.

Keywords

SemimoduleInclusion subsemimodule graphConnectivitydiameterClique number

Subject Classifications

16Y6005C7505C69

References

[1] S. Akbari, M. Habibi, A. Majidinya, R. Manaviyat, The inclusion ideal graph of rings, Comm. Algebra, 43(2015) 2457-2465
[2] A. H. Alwan, A. M. Alhossaini, Dedekind multiplication semimodules, Iraqi J. Sci., 61(6) (2020), 1488–1497.
[3] A. H. Alwan, Maximal submodule graph of a module, J. Discrete Math. Sci. Cryptogr., 24(7) (2021), 1941–1949.
[4] S. E. Atani & F. Saraei, On coatomic semimodules over commutative semirings, Cankaya Univ. J. Sci. Eng., 8(2011) 189-200
[5] I. Beck, coloring of commutative rings, J. Algebra,116(1988), 208-226.
[6] Bondy J.A., Murty U.S.R., Graph Theory, Graduate Texts in Mathematics, 244, Springer, 2008.
[7] J. Golan, semirings and their applications, Kluwer Academic Publ., 1999.
[8] J. Goswami, Submodule inclusion graph of a module, Adv. Math.: Sci. J., 9 (11) (2020), 9877–9886.
[9] Y. Katsov, T. Nam, N. Tuyen, On subtractive semisimple semirings, Algebra Colloq. 16(3) (2009), 415–426.
[10] Z. A. Nema & A. H. Alwan, Co-intersection graph of subsemimodules of a semimodule, Journal of Interdisciplinary Mathematics to appear.
[11] Parastoo Malakooti Rad & Lotf Ali Mahdavi (2019) A note on the intersection graph of submodules of a module, Journal of Interdisciplinary Mathematics, 22:4, 493-502, DOI: 10.1080/09720502.2019.1641896.
[12] R. A. Muneshwar & K. L. Bondar (2021) Automorphism group of the open subset inclusion graph of a topological space, Journal of Interdisciplinary Mathematics, 24:3, 657-665, DOI: 10.1080/09720502.2020.1848319.

Views: 182Downloads: 64Citations: 1