Upper dimension and bases of zero-divisor graphs of commutative rings
For a commutative ring with non-zero zero divisor set , the zero divisor graph of is with vertex set , where two distinct vertices and are adjacent if and only if . The upper dimension and the resolving number of a zero divisor graph of some rings are determined. We provide certain classes of rings...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2020-01-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1016/j.akcej.2018.12.001 |
| _version_ | 1818364011662540800 |
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| author | S. Pirzada M. Aijaz S.P. Redmond |
| author_facet | S. Pirzada M. Aijaz S.P. Redmond |
| author_sort | S. Pirzada |
| collection | DOAJ |
| description | For a commutative ring with non-zero zero divisor set , the zero divisor graph of is with vertex set , where two distinct vertices and are adjacent if and only if . The upper dimension and the resolving number of a zero divisor graph of some rings are determined. We provide certain classes of rings which have the same upper dimension and metric dimension and give an example of a ring for which these values do not coincide. Further, we obtain some bounds for the upper dimension in zero divisor graphs of commutative rings and provide a subset of vertices which cannot be excluded from any resolving set. |
| first_indexed | 2024-12-13T21:57:35Z |
| format | Article |
| id | doaj.art-96e1ee60806b40abb192a705425df00f |
| institution | Directory Open Access Journal |
| issn | 0972-8600 2543-3474 |
| language | English |
| last_indexed | 2024-12-13T21:57:35Z |
| publishDate | 2020-01-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | AKCE International Journal of Graphs and Combinatorics |
| spelling | doaj.art-96e1ee60806b40abb192a705425df00f2022-12-21T23:30:06ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002543-34742020-01-0117116817310.1016/j.akcej.2018.12.0011758513Upper dimension and bases of zero-divisor graphs of commutative ringsS. Pirzada0M. Aijaz1S.P. Redmond2Department of Mathematics, University of KashmirDepartment of Mathematics, University of KashmirDepartment of Mathematics and Statistics, Eastern Kentucky UniversityFor a commutative ring with non-zero zero divisor set , the zero divisor graph of is with vertex set , where two distinct vertices and are adjacent if and only if . The upper dimension and the resolving number of a zero divisor graph of some rings are determined. We provide certain classes of rings which have the same upper dimension and metric dimension and give an example of a ring for which these values do not coincide. Further, we obtain some bounds for the upper dimension in zero divisor graphs of commutative rings and provide a subset of vertices which cannot be excluded from any resolving set.http://dx.doi.org/10.1016/j.akcej.2018.12.001ringzero-divisor graphupper dimensionresolving number |
| spellingShingle | S. Pirzada M. Aijaz S.P. Redmond Upper dimension and bases of zero-divisor graphs of commutative rings AKCE International Journal of Graphs and Combinatorics ring zero-divisor graph upper dimension resolving number |
| title | Upper dimension and bases of zero-divisor graphs of commutative rings |
| title_full | Upper dimension and bases of zero-divisor graphs of commutative rings |
| title_fullStr | Upper dimension and bases of zero-divisor graphs of commutative rings |
| title_full_unstemmed | Upper dimension and bases of zero-divisor graphs of commutative rings |
| title_short | Upper dimension and bases of zero-divisor graphs of commutative rings |
| title_sort | upper dimension and bases of zero divisor graphs of commutative rings |
| topic | ring zero-divisor graph upper dimension resolving number |
| url | http://dx.doi.org/10.1016/j.akcej.2018.12.001 |
| work_keys_str_mv | AT spirzada upperdimensionandbasesofzerodivisorgraphsofcommutativerings AT maijaz upperdimensionandbasesofzerodivisorgraphsofcommutativerings AT spredmond upperdimensionandbasesofzerodivisorgraphsofcommutativerings |