Some Properties of the Complement of the Zero-Divisor Graph of a Commutative Ring | Zendy

S. Visweswaran | Zendy

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Some Properties of the Complement of the Zero-Divisor Graph of a Commutative Ring

Author(s) -

S. Visweswaran

Publication year - 2011

Publication title -

isrn algebra

Language(s) - English

Resource type - Journals

eISSN - 2090-6293

pISSN - 2090-6285

DOI - 10.5402/2011/591041

Subject(s) - zero divisor , mathematics , complement (music) , combinatorics , commutative ring , girth (graph theory) , graph , zero (linguistics) , ring (chemistry) , discrete mathematics , commutative property , biochemistry , chemistry , linguistics , philosophy , organic chemistry , gene , phenotype , complementation

Let R be a commutative ring with identity admitting at least two nonzero zero-divisors. Let (Γ()) denote the complement of the zero-divisor graph Γ() of . It is shown that if (Γ()) is connected, then its radius is equal to 2 and we also determine the center of (Γ()). It is proved that if (Γ()) is connected, then its girth is equal to 3, and we also discuss about its girth in the case when (Γ()) is not connected. We discuss about the cliques in (Γ()).

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