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arXiv · 2109.14108

Connected domination in grid graphs

Masahisa Goto·Koji M. Kobayashi
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Abstract

Given an undirected simple graph, a subset of the vertices of the graph is a {\em dominating set} if every vertex not in the subset is adjacent to at least one vertex in the subset. A subset of the vertices of the graph is a {\em connected dominating set} if the subset is a dominating set and the subgraph induced by the subset is connected. In this paper, we determine the minimum cardinality of a connected dominating set, called the {\em connected domination number}, of an $m \times n$ grid graph for any $m$ and $n$.

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Masahisa Goto, Koji M. Kobayashi. 2021-09-29. Connected domination in grid graphs. https://arxiv.org/abs/2109.14108

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