Lattice-Like Total Perfect Codes

Discussiones Mathematicae Graph Theory

Araujo Carlos¹  Dejter Italo² 

[1] Universidad del Atlántico Barranquilla, Colombia;University of Puerto Rico Rio Piedras, PR 00936-8377;

关键词: perfect dominating sets;    hypercubes;    lattices;   

DOI  :  10.7151/dmgt.1715

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown