Geodesic
Counting Maximal Distance-Independent Sets in Grid Graphs
Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 3, pp. 531-557

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Previous work on counting maximal independent sets for paths and certain 2-dimensional grids is extended in two directions: 3-dimensional grid graphs are included and, for some/any 𝓁∈ℕ, maximal distance-𝓁 independent (or simply: maximal 𝓁-independent) sets are counted for some grids. The transfer matrix method has been adapted and successfully applied
Keywords: independent set, grid graph, Fibonacci, Padovan numbers, transfer matrix method 
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Euler, Reinhardt; Oleksik, Paweł; Skupień, Zdzisław. Counting Maximal Distance-Independent Sets in Grid Graphs. Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 3, pp. 531-557. http://geodesic.mathdoc.fr/item/DMGT_2013_33_3_a4/