Domination and Total Domination Numbers in Zero-divisor Graphs of Commutative Rings
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910983440564224 |
|---|---|
| author | Anderson, Sarah Axtell, Mike Kroschel, Brenda Stickles, Joe |
| author_facet | Anderson, Sarah Axtell, Mike Kroschel, Brenda Stickles, Joe |
| contents | Zero-divisor graphs of commutative rings are well-represented in the literature. In this paper, we consider dominating sets, total dominating sets, domination numbers and total domination numbers of zero-divisor graphs. We determine the domination and total domination numbers of zero-divisor graphs are equal for all zero-divisor graphs of commutative rings except for $\mathbb{Z}_2 \times D$ in which $D$ is a domain. In this case, $γ(Γ(\mathbb{Z}_2 \times D)) = 1$ and $γ_t(Γ(\mathbb{Z}_2 \times D)) = 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02953 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Domination and Total Domination Numbers in Zero-divisor Graphs of Commutative Rings Anderson, Sarah Axtell, Mike Kroschel, Brenda Stickles, Joe Combinatorics 13A70, 05C69 Zero-divisor graphs of commutative rings are well-represented in the literature. In this paper, we consider dominating sets, total dominating sets, domination numbers and total domination numbers of zero-divisor graphs. We determine the domination and total domination numbers of zero-divisor graphs are equal for all zero-divisor graphs of commutative rings except for $\mathbb{Z}_2 \times D$ in which $D$ is a domain. In this case, $γ(Γ(\mathbb{Z}_2 \times D)) = 1$ and $γ_t(Γ(\mathbb{Z}_2 \times D)) = 2$. |
| title | Domination and Total Domination Numbers in Zero-divisor Graphs of Commutative Rings |
| topic | Combinatorics 13A70, 05C69 |
| url | https://arxiv.org/abs/2506.02953 |