Abstract
A contribution is made to the classification of lattice-like total perfect codes in integer latticesn via pairs (G,�) formed by abelian groups G and homomorphisms � : 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 inn with induced components that are parallel paths of length > 1 is posed as well.
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