The triple zero graph of a commutative ring

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dc.contributor.authorÇelikel, Ece Yetkin
dc.contributor.departmentOthertr_TR
dc.contributor.facultyOthertr_TR
dc.date.accessioned2022-12-21T07:51:58Z
dc.date.available2022-12-21T07:51:58Z
dc.date.issued2021
dc.description.abstractLet R be a commutative ring with non-zero identity. We define the set of triple zero elements of R by T Z ( R ) = { a ∈ Z ( R ) ∗ : there exists b , c ∈ R ∖ { 0 } such that a b c = 0 , a b ≠ 0 , a c ≠ 0 , b c ≠ 0 } . In this paper, we introduce and study some properties of the triple zero graph of R which is an undirected graph T Z Γ ( R ) with vertices T Z ( R ) , and two vertices a and b are adjacent if and only if a b ≠ 0 and there exists a non-zero element c of R such that a c ≠ 0 , b c ≠ 0 , and a b c = 0 . We investigate some properties of the triple zero graph of a general ZPI-ring R , we prove that d i a m ( T Z Γ ( R ) ) ∈ { 0 , 1 , 2 } and g r ( G ) ∈ { 3 , ∞ } .tr_TR
dc.description.indexTrdizintr_TR
dc.identifier.endpage663tr_TR
dc.identifier.issn/e-issn1303-5991
dc.identifier.issue2tr_TR
dc.identifier.startpage653tr_TR
dc.identifier.urihttps://doi.org/10.31801/cfsuasmas.786804tr_TR
dc.identifier.urihttp://hdl.handle.net/20.500.12575/86262
dc.identifier.volume70tr_TR
dc.language.isoentr_TR
dc.publisherAnkara Üniversitesitr_TR
dc.relation.isversionof10.31801/cfsuasmas.786804tr_TR
dc.relation.journalCommunications, Series A1:Mathematics and Statisticstr_TR
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Başka Kurum Yazarıtr_TR
dc.subjectTriple zero graph, Zero-divisor graph, 2-absorbing idealtr_TR
dc.titleThe triple zero graph of a commutative ringtr_TR
dc.typeArticletr_TR

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Cilt:70 Sayı:02 (2021)