Author
Koji M. Kobayashi
Bio: Koji M. Kobayashi is an academic researcher. The author has contributed to research in topics: Vertex (geometry) & Lattice graph. The author has co-authored 1 publications.
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TL;DR: In this article, the minimum cardinality of a connected dominating set, called the connected domination number (CDP), of an undirected simple graph was determined for any $m \times n$ grid graph.
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 $n$.