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- Title
Cycles in the Cozero-Divisor Graphs.
- Authors
Paknejad, N.; Erfanian, A.
- Abstract
Let R be a commutative ring with unity. The cozero-divisor graph of R denoted by Γ'(R) is a graph with vertex set W*(R), where W*(R) is the set of all non-zero and non-unit elements of R, and two distinct vertices a and b are adjacent if and only if a ∉ (b) and b ∉ (a). In this paper, we study the primitive cycle of cozero-divisor graphs and we determine all Artinian rings with claw-free or triangle-free cozero-divisor graphs. Also, we investigate all Artinian rings whose cozero-divisor graphs are C4-free.
- Subjects
DIVISOR theory; GRAPH theory; COMMUTATIVE rings; SET theory; TOPOLOGY
- Publication
Southeast Asian Bulletin of Mathematics, 2017, Vol 41, Issue 4, p547
- ISSN
0129-2021
- Publication type
Article