Further Results on the Majority Roman Domination in graphs
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866918234882572288 |
|---|---|
| author | Emadi, Azam Sadat Masoumi, Iman Musawi, Seyed Reza |
| author_facet | Emadi, Azam Sadat Masoumi, Iman Musawi, Seyed Reza |
| contents | Let $G=(V,E)$ be a simple graph of order $n$. A Majority Roman Dominating Function (MRDF) on a graph G is a function $f: V\rightarrow\{-1, +1, 2\}$ if the sum of its function values over at least half the closed neighborhoods is at least one , this is , for at least half of the vertices $v\in V$, $f(N[v])\geq 1$. Moreover, every vertex u with $f(u)=-1$ is adjacent to at least one vertex $w$ with $f(w)=2$. The Majority Roman Domination number of a graph $G$, denoted by $γ_{MR}(G)$ , is the minimum value of $\sum_{v\in{V(G)}}f(v)$ over all Majority Roman Dominating Function $f$ of $G$. In this paper we study properties of the Majority Roman Domination in graphs and obtain lower and upper bounds the Majority Roman Domination number of some graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07266 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Further Results on the Majority Roman Domination in graphs Emadi, Azam Sadat Masoumi, Iman Musawi, Seyed Reza Combinatorics Let $G=(V,E)$ be a simple graph of order $n$. A Majority Roman Dominating Function (MRDF) on a graph G is a function $f: V\rightarrow\{-1, +1, 2\}$ if the sum of its function values over at least half the closed neighborhoods is at least one , this is , for at least half of the vertices $v\in V$, $f(N[v])\geq 1$. Moreover, every vertex u with $f(u)=-1$ is adjacent to at least one vertex $w$ with $f(w)=2$. The Majority Roman Domination number of a graph $G$, denoted by $γ_{MR}(G)$ , is the minimum value of $\sum_{v\in{V(G)}}f(v)$ over all Majority Roman Dominating Function $f$ of $G$. In this paper we study properties of the Majority Roman Domination in graphs and obtain lower and upper bounds the Majority Roman Domination number of some graphs. |
| title | Further Results on the Majority Roman Domination in graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2411.07266 |