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: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2020-01-01
|
| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1016/j.akcej.2018.12.001 |
| Summary: | 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. |
|---|---|
| ISSN: | 0972-8600 2543-3474 |