Geodesic
Lattice-Like Total Perfect Codes
Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 1, pp. 57-74

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A contribution is made to the classification of lattice-like total perfect codes in integer lattices Λ_n via pairs (G, Φ) formed by abelian groups G and homomorphisms Φ: Z^n → G. A conjecture is posed that the cited contribution covers all possible cases. A related conjecture on the unfinished work on open problems on lattice-like perfect dominating sets in Λ_n with induced components that are parallel paths of length gt; 1 is posed as well.
Keywords: perfect dominating sets, hypercubes, lattices 
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Araujo, Carlos; Dejter, Italo. Lattice-Like Total Perfect Codes. Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 1, pp. 57-74. http://geodesic.mathdoc.fr/item/DMGT_2014_34_1_a4/