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http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/6410| Title: | On Weakly Perfect Annihilating-Ideal Graphs |
| Authors: | Kadu, Ganesh S. Joshi, Vinayak GONDE, SAMRUDDHA Dept. of Mathematics |
| Keywords: | Annihilating-ideal graph Semigroup Semiprime ideal Weakly perfect graph Zero-divisor graph 2021-NOV-WEEK4 TOC-NOV-2021 2021 |
| Issue Date: | Dec-2021 |
| Publisher: | Cambridge University Press |
| Citation: | Bulletin of the Australian Mathematical Society, 104(3), 362-372. |
| 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. |
| URI: | http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/6410 https://doi.org/10.1017/S0004972721000265 |
| ISSN: | 0004-9727 1755-1633 |
| Appears in Collections: | JOURNAL ARTICLES |
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