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Journal of Discrete Mathematical Sciences and Cryptography

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

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Journal of Discrete Mathematical Sciences and Cryptography
Open Access Research Article

M-polynomial of prime graph of commutative ring Zp2, Z2p and Zpq

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pp. 2013–2018Vol. 29Issue 5May 2026DOI: 10.47974/JDMSC-2383 Crossmark XML
Received:
01 May 2025
Published Online:
22 May 2026
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2383
Pages:
2013–2018

Abstract

This study examines the Mpolynomial defined by M(G; α, β) = ∑i ≤ j mij (G)αi βj of the prime graph associated with certain Commutative rings. The M-polynomial is a tool in graph theory that encodes details about the degrees of edges in a graph. The study defines the primegraph structure of a Commutative ring Zp2, Z2p and Zpq and calculates its M polynomial for several specific rings. The results include detailed theorems and proofs demonstrating how the M polynomial can be derived according to the degree sequences of the vertices in the prime graph. Examples are provided for different rings to illustrate the computation method. The work contributes to the ongoing research connecting algebraic structures, particularly Commutative rings, with graph-theoretic concepts.

Keywords

Prime graphM polynomialCommutative ringGraph theory

Subject Classifications

05C2513A99

References

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