On Weakly Perfect Annihilating-Ideal Graphs

Kadu, Ganesh S.; Joshi, Vinayak; GONDE, SAMRUDDHA

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dc.contributor.author	Kadu, Ganesh S.	en_US
dc.contributor.author	Joshi, Vinayak	en_US
dc.contributor.author	GONDE, SAMRUDDHA	en_US
dc.date.accessioned	2021-11-29T10:52:27Z
dc.date.available	2021-11-29T10:52:27Z
dc.date.issued	2021-12	en_US
dc.identifier.citation	Bulletin of the Australian Mathematical Society, 104(3), 362-372.	en_US
dc.identifier.issn	0004-9727	en_US
dc.identifier.issn	1755-1633	en_US
dc.identifier.uri	http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/6410
dc.identifier.uri	https://doi.org/10.1017/S0004972721000265	en_US
dc.description.abstract	We prove that the annihilating-ideal graph of a commutative semigroup with unity is, in general, not weakly perfect. This settles the conjecture of DeMeyer and Schneider [‘The annihilating-ideal graph of commutative semigroups’, J. Algebra 469 (2017), 402–420]. Further, we prove that the zero-divisor graphs of semigroups with respect to semiprime ideals are weakly perfect. This enables us to produce a large class of examples of weakly perfect zero-divisor graphs from a fixed semigroup by choosing different semiprime ideals.	en_US
dc.language.iso	en	en_US
dc.publisher	Cambridge University Press	en_US
dc.subject	Annihilating-ideal graph	en_US
dc.subject	Semigroup	en_US
dc.subject	Semiprime ideal	en_US
dc.subject	Weakly perfect graph	en_US
dc.subject	Zero-divisor graph	en_US
dc.subject	2021-NOV-WEEK4	en_US
dc.subject	TOC-NOV-2021	en_US
dc.subject	2021	en_US
dc.title	On Weakly Perfect Annihilating-Ideal Graphs	en_US
dc.type	Article	en_US
dc.contributor.department	Dept. of Mathematics	en_US
dc.identifier.sourcetitle	Bulletin of the Australian Mathematical Society	en_US
dc.publication.originofpublisher	Foreign	en_US