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arXiv · 1311.4476

Critical properties on Roman domination graphs

A. Martínez-Pérez·D. Oliveros
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Abstract

A Roman domination function on a graph G is a function $r:V(G)\to \{0,1,2\}$ satisfying the condition that every vertex $u$ for which $r(u)=0$ is adjacent to at least one vertex $v$ for which $r(v)=2$. The weight of a Roman function is the value $r(V(G))=\sum_{u\in V(G)}r(u)$. The Roman domination number $\gamma_R(G)$ of $G$ is the minimum weight of a Roman domination function on $G$. "Roman Criticality" has been defined in general as the study of graphs where the Roman domination number decreases when removing an edge or a vertex of the graph. In this paper we give further results in this topic as well as the complete characterization of critical graphs that have Toman Domination number $\gamma_R(G)=4$.

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A. Martínez-Pérez, D. Oliveros. 2013-11-18. Critical properties on Roman domination graphs. https://arxiv.org/abs/1311.4476

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