Fibonacci-run graphs II: Degree sequences

Eğecioǧlu, Ömer; Iršič, Vesna

doi:10.1016/j.dam.2021.05.018

Cited by 7 publications

(1 citation statement)

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“…More generally, the generating function of the up-down degree enumerator polynomials for R n would give Proposition 7.1 and Proposition 7.2 as corollaries, and provide the generating function for the degree enumerator polynomials itself for u = d = x. The derivation of this general case is of independent interest and is studied in detail in a companion paper [3].…”

Section: Up-down Degree Sequencesmentioning

confidence: 99%

Fibonacci-run graphs I: basic properties

Eğecioǧlu¹,

Iršič²

2020

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Among the classical models for interconnection networks are hypercubes and Fibonacci cubes. Fibonacci cubes are induced subgraphs of hypercubes obtained by restricting the vertex set to those binary strings which do not contain consecutive 1s, counted by Fibonacci numbers. Another set of binary strings which are counted by Fibonacci numbers are those with a restriction on the runlengths. Induced subgraphs of the hypercube on the latter strings as vertices define Fibonacci-run graphs. They have the same number of vertices as Fibonacci cubes, but fewer edges and different connectivity properties.We obtain properties of Fibonacci-run graphs including the number of edges, the analogue of the fundamental recursion, the average degree of a vertex, Hamiltonicity, special degree sequences, the number of hypercubes they contain, and show that they are partial cubes. A detailed study of the degree sequences of Fibonacci-run graphs is interesting in its own right and is reported in a companion paper.

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Section: Up-down Degree Sequencesmentioning

confidence: 99%