A note on total graph of commutative krasner hyperrings

Document Type : Research Paper

Authors

1 ‎Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran

2 Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran

3 Fouman Faculty of Engineering, College of Engineering, University of Tehran, Fouman, Iran

Abstract

The purpose of this paper is to introduce the notion of total graph of Krasner hyperrings. In this regard, a connection between the graph theory and the theory of hyperrings is constructed and some fundamental properties of the total graph of Krasner hyperrings are investigated. Finally, for a multiplicative-prime subset $H$ of a hyperring $R$, the diameter and the girth of $\Gamma_{\!\!H}(R\setminus H)\,\mbox{and}\, \Gamma_{\!\!H}(H)$ are computed precisely.

Keywords

References

[1] R. Ameri, M. Hamidi and H. Mohammadi, Hyperideals of (finite) general hyperrings, Mathematics Interdisciplinary Research, (4) 6 (2021), 257-273.
[2] D. F. Anderson, T. Asir, A. Badawi and T. T. Chelvam, Graphs from Rings, New York, NY, USA: Springer International Publishing, 2021.
[3] D. F. Anderson and A. Badawi, The generalized total graph of a commutative ring, Journal of Algebra and Its Applications, (5) 12 (2013), 1250212.
[4] A. Asokkumar, Derivations in hyperrrings and prime hyperrings, Iranian Journal of Mathematical Sciences and Informatics, (1) 8 (2013), 1-13.
[5] B. Davvaz and V. Leoreanu-Fotea, Hyperring Theory and Applications, International Academic Press, USA, 2007.
[6] F. Esmaeili Khalil Saraei, H. Heydarinejad Astaneh and R. Navidinia, The total graph of a module with respect to multiplicative-prime subsets, Rom. J. Math. Comput. Sci, (2) 4 (2014), 151-166.
[7] F. Esmaeili Khalil Saraei and E. Navidinia, On the extended total graph of modules over commutativerings, International Electronic Journal of Algebra, 25 (2019), 77-86.
[8] F. Esmaeili Khalil Saraei and E. Navidinia, A note on the extended total graph of commutative rings, Journal of Algebra and Related Topics, (1) 6 (2018), 25-33.
[9] M. Hamidi, R. Ameri and H. Mohammadi, Hyperideal-based intersection graphs, Indian J. Pure Appl Math, (1) 54 (2022), 120-132.
[10] L. Kamali Ardekani and B. Davvaz, A generalization of prime hyperideals in Krasner hyperrings, Journal of Algebraic Systems, (2) 7 (2020), 205-216.
[11] M. Krasner, Approximation des corps values complets de caracteristique p, p > 0, par ceux de caracteristique zero, Colloque d′ Algebre Superieure (Bruxelles, Decembre 1956), CBRM, Bruxelles, (1957).
[12] F. Marty, Sur une generalization de la notion de groupe, 8th Congres Math. Scandinaves, Stockholm, Sweden (1934), 45-49.
Journal of Algebra and Related Topics
Volume 13, Issue 1
July 2025
Pages 87-97

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