The embedding of line graphs associated to the annihilator graph of commutative rings
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910648100716544 |
|---|---|
| author | Shariq, Mohd Mathil, Praveen Nazim, Mohd Kumar, Jitender |
| author_facet | Shariq, Mohd Mathil, Praveen Nazim, Mohd Kumar, Jitender |
| contents | The annihilator graph $AG(R)$ of the commutative ring $R$ is an undirected graph with vertex set as the set of all non-zero zero divisors of $R$, and two distinct vertices $x$ and $y$ are adjacent if and only if $ann(xy) \neq ann(x) \cup ann(y)$. In this paper, we study the embedding of the line graph of $AG(R)$ into orientable or non-orientable surfaces. We completely characterize all the finite commutative rings such that the line graph of $AG(R)$ is of genus or crosscap at most two. We also obtain the inner vertex number of $L(AG(R))$. Finally, we classify all the finite rings such that the book thickness of $L(AG(R))$ is at most four. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_18671 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The embedding of line graphs associated to the annihilator graph of commutative rings Shariq, Mohd Mathil, Praveen Nazim, Mohd Kumar, Jitender Combinatorics Rings and Algebras 05C25, 13A70 The annihilator graph $AG(R)$ of the commutative ring $R$ is an undirected graph with vertex set as the set of all non-zero zero divisors of $R$, and two distinct vertices $x$ and $y$ are adjacent if and only if $ann(xy) \neq ann(x) \cup ann(y)$. In this paper, we study the embedding of the line graph of $AG(R)$ into orientable or non-orientable surfaces. We completely characterize all the finite commutative rings such that the line graph of $AG(R)$ is of genus or crosscap at most two. We also obtain the inner vertex number of $L(AG(R))$. Finally, we classify all the finite rings such that the book thickness of $L(AG(R))$ is at most four. |
| title | The embedding of line graphs associated to the annihilator graph of commutative rings |
| topic | Combinatorics Rings and Algebras 05C25, 13A70 |
| url | https://arxiv.org/abs/2409.18671 |