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Induced subgraphs of zero-divisor graphs
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dc.contributor.author | Arunkumar, G | |
dc.contributor.author | Cameron, Peter J. | |
dc.contributor.author | Kavaskar, T. | |
dc.contributor.author | Chelvam, T. Tamizh | |
dc.date.accessioned | 2023-06-27T11:30:07Z | |
dc.date.available | 2023-06-27T11:30:07Z | |
dc.date.issued | 2023-10-01 | |
dc.identifier | 287686088 | |
dc.identifier | 3551b0c3-5c78-41b4-a7b0-91d7ef065523 | |
dc.identifier | 85162784575 | |
dc.identifier.citation | Arunkumar , G , Cameron , P J , Kavaskar , T & Chelvam , T T 2023 , ' Induced subgraphs of zero-divisor graphs ' , Discrete Mathematics , vol. 346 , no. 10 , 113580 . https://doi.org/10.1016/j.disc.2023.113580 | en |
dc.identifier.issn | 0012-365X | |
dc.identifier.other | ORCID: /0000-0003-3130-9505/work/137914943 | |
dc.identifier.uri | https://hdl.handle.net/10023/27811 | |
dc.description | Funding: Peter J. Cameron acknowledges the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Groups, representations and applications: new perspectives (supported by EPSRC grant no. EP/R014604/1), where he held a Simons Fellowship. For this research, T. Kavaskar was supported by the University Grant Commissions Start-Up Grant, Government of India grant No. F. 30-464/2019 (BSR) dated 27.03. T. Tamizh Chelvam was supported by CSIR Emeritus Scientist Scheme (No. 21 (1123)/20/EMR-II) of Council of Scientific and Industrial Research, Government of India. | en |
dc.description.abstract | The zero-divisor graph of a finite commutative ring with unity is the graph whose vertex set is the set of zero-divisors in the ring, with a and b adjacent if ab=0. We show that the class of zero-divisor graphs is universal, in the sense that every finite graph is isomorphic to an induced subgraph of a zero-divisor graph. This remains true for various restricted classes of rings, including boolean rings, products of fields, and local rings. But in more restricted classes, the zero-divisor graphs do not form a universal family. For example, the zero-divisor graph of a local ring whose maximal ideal is principal is a threshold graph; and every threshold graph is embeddable in the zero-divisor graph of such a ring. More generally, we give necessary and sufficient conditions on a non-local ring for which its zero-divisor graph to be a threshold graph. In addition, we show that there is a countable local ring whose zero-divisor graph embeds the Rado graph , and hence every finite or countable graph, as induced subgraph. Finally, we consider embeddings in related graphs such as the 2-dimensional dot product graph. | |
dc.format.extent | 9 | |
dc.format.extent | 311408 | |
dc.language.iso | eng | |
dc.relation.ispartof | Discrete Mathematics | en |
dc.subject | Zero divisor | en |
dc.subject | Local ring | en |
dc.subject | Universal graph | en |
dc.subject | Rado graph | en |
dc.subject | QA Mathematics | en |
dc.subject | Mathematics(all) | en |
dc.subject | T-NDAS | en |
dc.subject | MCC | en |
dc.subject.lcc | QA | en |
dc.title | Induced subgraphs of zero-divisor graphs | en |
dc.type | Journal article | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.identifier.doi | 10.1016/j.disc.2023.113580 | |
dc.description.status | Peer reviewed | en |
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