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#### Article Title

Restrained reinforcement number in graphs

July 2022

#### Abstract

A set $S$ of vertices is a restrained dominating set of a graph $G=(V,E)$ if every vertex in $V\setminus S$ has a neighbor in $S$ and a neighbor in $V\setminus S$. The minimum cardinality of a restrained dominating set is the restrained domination number $\gamma_{r}(G)$. In this paper we initiate the study of the restrained reinforcement number $r_{r}(G)$ of a graph $G$ defined as the cardinality of a smallest set of edges $F\subseteq E(\overline{G})$ for which \$\gamma _{r}(G+F)

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Supplemental Reference List with DOIs

COinS

#### DOI

https://doi.org/10.20429/tag.2022.090209