DOI: https://doi.org/10.14710/jfma.v9i1.30612

M-Polynomial of Regular Divisor Graph of Finite Commutative Ring

*Payman Abbas Rashed orcid scopus  -  Salahuddin University/ Collage of Basic Education/ Mathematical Departments/ Erbil -Iraq, Iraq
Mohammed N Authman  -  Department of Mathematics, Open Educational College, Ninawa Directorate of Education, Iraqi Ministry of Education, Iraq

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Abstract
Let R be a finite commutative ring with identity, for all non-zero elements a and b in the ring R are adjacent if and only if a=a.b.a or b=b.a.b and a≠b , this graph is called by regular divisor graph and denoted by ℜ∂(R), with vertex set V(ℜ∂(R)) consists of elements of r∗(R)=Reg(R)−{0} and edge set E(ℜ∂(R))={(a,b)∶a=a.b.a or b=b.a.b ,a≠b≠0,a,bReg(R)−{0} } . We classify the finite commutative ring to get a special graph and we are going to study some properties of this graph, up to the R which is local, Boolean and field. And we study the M-polynomial of the regular divisor graph ℜ∂(R), and the general form of regulardivisor graph of R=Zp×Zq for any prime number p and q. In this paper we got somenew results with appear with the new graph.
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Keywords: Regular divisor graph, M- polynomial, Cross product of fields Zp×Zq.

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Section: FUNDAMENTAL MATHEMATICS AND APPLICATIONS
Language : EN
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