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RESTRAINED WEAKLY CONNECTED 2-DOMINATION IN GRAPHS
Keywords:
weakly connected domination, 2-domination, restrained weakly connected 2-domination.DOI:
https://doi.org/10.17654/0974165822029Abstract
Let $G=(V(G), E(G))$ be a connected graph. A restrained weakly connected 2-dominating set in $G$ is a set $D$ of vertices in $G$ such that every vertex in $V(G) \backslash D$ is dominated by at least two vertices in $D$ and is adjacent to at least one vertex in $V(G) \backslash D$ and that the subgraph $\langle D\rangle_w$ weakly induced by $D$ is connected. The restrained weakly connected 2-domination number of $G$, denoted by $\gamma_{r 2 w}(G)$, is the smallest cardinality of a restrained weakly connected 2-dominating set in $G$. In this paper, we study this new parameter and obtain some general results. Furthermore, we also generate closed formulas for the restrained weakly connected 2-domination numbers of some families of graphs.
Received: April 7, 2022
Accepted: May 19, 2022
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