A contribution is made to the classification of lattice-like total perfect codes in integer lattices Λn via pairs (G, Φ) formed by abelian groups G and homomorphisms Φ: Zn → 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 Λn with induced components that are parallel paths of length > 1 is posed as well.
@article{bwmeta1.element.doi-10_7151_dmgt_1715,
author = {Carlos Araujo and Italo Dejter},
title = {Lattice-Like Total Perfect Codes},
journal = {Discussiones Mathematicae Graph Theory},
volume = {34},
year = {2014},
pages = {57-74},
zbl = {1292.94181},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1715}
}
Carlos Araujo; Italo Dejter. Lattice-Like Total Perfect Codes. Discussiones Mathematicae Graph Theory, Tome 34 (2014) pp. 57-74. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1715/
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