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Asymptotic properties of Fibonacci cubes and Lucas cubesKlavžar, Sandi ; Mollard, MichelDokazano je, da imajo Fibonaccijeve kocke in Lucasove kocke asimptotično povprečno ekscentričnost enako ▫$(5+\sqrt 5)/10$▫ in asimptotično povprečno stopnjo enako ▫$(5-\sqrt 5)/5$▫. Vpeljano je novo ... označevanje Fibonaccijevih dreves in dokazano je, da je ekscentričnost vozlišča dane Fibonaccijeve kocke enaka globini prirejenega lista v pripadajočem Fibonaccijevem drevesu. Vpeljana in študirana je hiperkockina gostota. Za Fibonaccijeve kocke in Lucasove kocke je dokazano, da je ta gostota enaka ▫$(1-1/\sqrt 5)/\log_2\varphi$▫, kjer je ▫$\varphi$▫ razmerje zlatega reza. S pomočjo kartezičnega produkta grafov so konstruirane družine grafov s fiksno, neničelno gostoto. Dokazano je tudi, da povprečno razmerje števila Fibonaccijevih nizov, ki imajo 0 oz. 1 na danem mestu, in kjer je povprečje narejeno preko vseh mest, konvergira k ▫$\varphi^2$▫. Podobno je narejeno tudi za Lucasove kocke.Source: Annals of combinatorics. - ISSN 0218-0006 (Vol. 18, no. 3, 2014, str. 447-457)Type of material - article, component part ; adult, seriousPublish date - 2014Language - englishCOBISS.SI-ID - 17087065
Author
Klavžar, Sandi |
Mollard, Michel
Topics
teorija grafov |
Fibonaccijeve kocke |
Lucasove kocke |
konvergenca zaporedij |
povprečna ekscentričnost |
Fibonaccijevo drevo |
povprečna stopnja |
hiperkockina gostota |
graph theory |
Fibonacci cubes |
Lucas cubes |
convergence of sequences |
average eccentricity |
Fibonacci tree |
average degree |
hypercube density
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Klavžar, Sandi | 05949 |
Mollard, Michel | ![]() |
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