2022
DOI: 10.24996/ijs.2022.63.2.21
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Idempotent Divisor Graph of Commutative Ring

Abstract: This work aims to introduce and to study a new kind of divisor graph which is  called idempotent divisor graph, and it is  denoted by . Two non-zero distinct vertices v1 and v2 are adjacent if and only if , for some non-unit idempotent element . We establish some fundamental properties of ,  as well as it’s connection with . We also study planarity of this graph.

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Cited by 3 publications
(2 citation statements)
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“…In this paper, we generalized the Schultz polynomial and modified the Schultz polynomial by taking all vertices degrees of the path, provided that the product of the length of the path with the sum of the degrees is a minimum, because of the importance of degrees as chemical bonds located on atoms and they are effects on the stability of the chemical compound. Finally, there are many indices and many polynomials which are important in knowing the chemical and physical properties of chemical compounds, see [12][13][14][15][16][17] .…”
Section: Najm and Alimentioning
confidence: 99%
“…In this paper, we generalized the Schultz polynomial and modified the Schultz polynomial by taking all vertices degrees of the path, provided that the product of the length of the path with the sum of the degrees is a minimum, because of the importance of degrees as chemical bonds located on atoms and they are effects on the stability of the chemical compound. Finally, there are many indices and many polynomials which are important in knowing the chemical and physical properties of chemical compounds, see [12][13][14][15][16][17] .…”
Section: Najm and Alimentioning
confidence: 99%
“…Also, there are many other definitions that connect these two theories of graph and ring, for example see [5][6][7]. In 2021, Mohammad and Shuker [8], gave the definition of the idempotent divisor graph of commutative ring R with identity 1 , it is a graph denoted by Л(R) which has vertices set in R* = R-{0}, and for any distinct vertices x and y, x adjacent with y if and only if x.y = e for some non-unit idempotent element e 2 = e in R. If R is a local ring, then the only non-unit idempotent element in R is zero, they assumed that V(Л(R))=Z(R) * , this means that Л(R)= (R). Furthermore they presented some fundamental properties of this graph, and they studied planarity of this graph.…”
Section: Introductionmentioning
confidence: 99%