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arXiv · 2411.07266

Further Results on the Majority Roman Domination in graphs

Azam Sadat Emadi·Iman Masoumi·Seyed Reza Musawi
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Abstract

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 $\gamma_{MR}(G)$ , 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.

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Azam Sadat Emadi, Iman Masoumi, Seyed Reza Musawi. 2024-11-09. Further Results on the Majority Roman Domination in graphs. https://arxiv.org/abs/2411.07266

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