Title : ( Common zero-divisor graph over a commutative ring )
Authors: fazlahmad abbasnia , Kazem Khashyarmanesh , Ahmad Erfanian ,
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Abstract
Let R be a finite commutative ring with non-zero identity and Z(R)∗ be the set of all non-zero zero-divisors of R. In this paper, for a non-empty subset S of Z(R)∗, we introduce a new graph, denoted by Γ(R, S), with vertex set Z(R)∗ and two distinct vertices x and y are adjacent if and only if there is s ∈ S such that sx = 0 = sy. Then, we investigate some properties of the graph Γ(R, S)
Keywords
, Zero, divisor graph; common zero, divisor graph; Cayley graph; connectivity; regularity
@article{paperid:1098209,
author = {Abbasnia, Fazlahmad and Khashyarmanesh, Kazem and Erfanian, Ahmad},
title = {Common zero-divisor graph over a commutative ring},
journal = {Asian-European Journal of Mathematics},
year = {2024},
volume = {17},
number = {1},
month = {January},
issn = {1793-5571},
keywords = {Zero-divisor graph; common zero-divisor graph; Cayley graph; connectivity;
regularity},
}
%0 Journal Article
%T Common zero-divisor graph over a commutative ring
%A Abbasnia, Fazlahmad
%A Khashyarmanesh, Kazem
%A Erfanian, Ahmad
%J Asian-European Journal of Mathematics
%@ 1793-5571
%D 2024
