Geodesic
Bounds on Watching and Watching Graph Products
Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 1, pp. 63-79

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A watchman’s walk for a graph G is a minimum-length closed dominating walk, and the length of such a walk is denoted (G). We introduce several lower bounds for such walks, and apply them to determine the length of watchman’s walks in several grids.
Keywords: watchman’s walk, domination, graph products 
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Dyer, Danny; Howell, Jared. Bounds on Watching and Watching Graph Products. Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 1, pp. 63-79. http://geodesic.mathdoc.fr/item/DMGT_2022_42_1_a4/