On domination-type invariants of Fibonacci cubes and hypercubes
Azarija, Jernej, 1988- ...
Fibonaccijeva kocka ▫$\Gamma_n$▫ je podgraf ▫$n$▫-dimenzionalne kocke ▫$Q_n$▫ induciran z vozlišči, ki ne vsebujejo dveh zaporednih enic. S pomočjo celoštevilskega linearnega programiranja določimo ...točne vrednosti za ▫$\gamma_t(\Gamma_n)$▫, ▫$n\le 12$▫. Kot posledico dokažemo, da za vse ▫$n\ge 11$▫ velja ▫$\gamma_t(\Gamma_{n})\le 2F_{n-10} + 21F_{n-8}$▫, kjer so ▫$F_n$▫ Fibonaccijeva števila. Dokazano je tudi, da če je ▫$n\ge 9$▫, potem velja ▫$\gamma_t(\Gamma_{n}) \ge \left\lceil (F_{n+2}-11)/(n-3)\right\rceil - 1$▫. S pomočjo celoštevilskega linearnega programiranja so določene točne vrednosti za 2-pakirno število, povezano dominantno število, dvojno dominantno število in predznačeno dominantno število majhnih Fibonaccijevih kock in hiperkock. Domneva za celotno dominantno število hiperkock, ki trdi, da za vse ▫$n \geq 6$▫ velja ▫$\gamma_t(Q_n) = 2^{n-2}$▫, je ovržena na več različnih načinov.
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