Fibonaccijeve kocke so inducirani podgrafi hiperkock, ki jih dobimo tako, da množico vozlišč zožimo le na tiste dvojiške nize, ki ne vsebujejo zaporednih enic. Ti podgrafi so bili veliko študirani ...tako v svoji osnovni obliki kot tudi v drugih različicah. Inducirani podgrafi hiperkock na dvojiških nizih z restrikcijo na dolžino blokov enic kot vozliščih definirajo Fibonacci-run grafe. Ti grafi imajo enako število vozlišč kot Fibonaccijeve kocke, ampak manj povezav in drugačne grafovske lastnosti. Osnovne lastnosti Fibonacci-run grafov so predstavljene v [O. Eğecioğlu, V. Iršič, Fibonacci-run graphs I: basic properties, Discrete Appl. Math. 295 (2021) 70-84], med tem ko se v tem članku osredotočimo na vozliščna zaporedja Fibonacci-run grafov. Rodovna funkcija, ki natančno opisuje vozliščna zaporedja, ima več posledic. Opišemo tudi lastnosti Fibonacci-run grafov gledanih kot delno urejene množice in študiramo vložitve Fibonacci-run grafov.
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