Geodesic
Quasiperfect domination in triangular lattices
Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 1, pp. 179-198

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A vertex subset S of a graph G is a perfect (resp. quasiperfect) dominating set in G if each vertex v of G∖S is adjacent to only one vertex (d_v ∈ 1,2 vertices) of S. Perfect and quasiperfect dominating sets in the regular tessellation graph of Schläfli symbol 3,6 and in its toroidal quotients are investigated, yielding the classification of their perfect dominating sets and most of their quasiperfect dominating sets S with induced components of the form K_ν, where ν ∈ 1,2,3 depends only on S.
Keywords: perfect dominating set, quasiperfect dominating set, triangular lattice 
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Dejter, Italo. Quasiperfect domination in triangular lattices. Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 1, pp. 179-198. http://geodesic.mathdoc.fr/item/DMGT_2009_29_1_a10/