Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.07510 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910737638621184 |
|---|---|
| author | Kumar, Ravindra Prakash, Om |
| author_facet | Kumar, Ravindra Prakash, Om |
| contents | For a graph $G= (V, E)$, a Roman dominating function is a map $f : V \rightarrow \{0, 1, 2\}$ satisfies the property that if $f(v) = 0$, then $v$ must have adjacent to at least one vertex $u$ such that $f(u)= 2$. The weight of a Roman dominating function $f$ is the value $f(V)= Σ_{u \in V} f(u)$, and the minimum weight of a Roman dominating function on $G$ is called the Roman domination number of $G$, denoted by $γ_R(G)$. The main focus of this paper is to study the Roman domination number of zero-divisor graph $Γ(R)$ and find the bounds of the Roman domination number of $T(Γ(R))$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07510 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Roman domination number of zero-divisor graphs over commutative rings Kumar, Ravindra Prakash, Om Combinatorics 13M99, 05C25 For a graph $G= (V, E)$, a Roman dominating function is a map $f : V \rightarrow \{0, 1, 2\}$ satisfies the property that if $f(v) = 0$, then $v$ must have adjacent to at least one vertex $u$ such that $f(u)= 2$. The weight of a Roman dominating function $f$ is the value $f(V)= Σ_{u \in V} f(u)$, and the minimum weight of a Roman dominating function on $G$ is called the Roman domination number of $G$, denoted by $γ_R(G)$. The main focus of this paper is to study the Roman domination number of zero-divisor graph $Γ(R)$ and find the bounds of the Roman domination number of $T(Γ(R))$. |
| title | Roman domination number of zero-divisor graphs over commutative rings |
| topic | Combinatorics 13M99, 05C25 |
| url | https://arxiv.org/abs/2412.07510 |