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13.
Fibonaccijeve kocke : magistrsko delo
Jamnikar, Anita
V magistrskem delu proučujemo Fibonaccijeve kocke, ki so bile vpeljane leta 1993 in so bile takrat intezivno proučevane. Fibonaccijev niz je binarni niz, v katerem ni dveh zaporednih enic. ...Fibonaccijeva kocka ▫$\Gamma_{n}, n \geq, \ge0$▫ je definirana kot graf ▫$(V_n, E_n)$▫ z množico vozlišč ▫$V_{n}(\Gamma_{n} = \lbrace 0,1 ..., F_{n+2} - 1\rbrace$▫, kjer sta vozlišči sosednji natanko takrat, ko je Hammingova razdalja njunih Fibonaccijevih nizov enaka 1. Na začetku spoznamo Zeckendorfov izrek, osnove definicije, strukturne in numerične lastnosti Fibonaccijevih kock. V nadaljevanju so predstavljene nekatere invariante kot so hamiltonskost, neodvisno število, ▫$\theta$▫-gracilne označitve, opazovalno in deciklično število. V osrednjem delu je dokazano, da so Fibonaccijeve kocke natanko resonančni grafi fibonaccenov. Karakterizirani so tudi dvodelni ravninski grafi, katerih resonančni grafi so Fibonaccijeve kocke. Nadalje sta predstavljeni dve karakterizaciji Fibonaccijevih kock. Ti karakterizaciji sta osnova algoritmov,ki prepoznajo Fibonaccijevek kocke v času O(mn) in O(m log n). Za zaključek predstavimo Lucasove kocke in pregledamo nekaj rezultatov o posplošenih Fibonaccijevih kockah.
Type of material - master's thesis
; adult, serious
Publication and manufacture - Maribor : [A. Jamnikar], 2010
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