The cozero-divisor graph relative to finitely generated modules

Ansari-Toroghy, H.; Farshadifar, F.; Habibi, Sh.

doi:10.18514/mmn.2013.762

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“…Akbari et al gave further results on rings with forest cozero-divisor graphs and diameter of cozero-divisor graphs associated with R[x] and R[[x]] (see [6]). The cozero-divisor graph has also been studied in several other papers (e.g., [5,7,8,12]). In this paper, we deal with the coloring cozero-divisor graphs problem.…”

Section: Introductionmentioning

confidence: 99%

Coloring of cozero-divisor graphs of commutative von Neumann regular rings

Nikandish¹,

Nikmehr²,

Bakhtyiari³

2018

Preprint

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Let R be a commutative ring with non-zero identity. The cozero-divisor graph of R, denoted by Γ ′ (R), is a graph with vertices in W * (R), which is the set of all non-zero and non-unit elements of R, and two distinct vertices a and b in W * (R) are adjacent if and only if a ∈ Rb and b ∈ Ra. In this paper, we show that the cozero-divisor graph of a von Neumann regular ring with finite clique number is not only weakly perfect but also perfect. Also, an explicit formula for the clique number is given.

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