Fibonacci-run graphs II: Degree sequences

Fibonacci cubes are induced subgraphs of hypercube graphs obtained by restricting the vertex set to those binary strings which do not contain consecutive 1s. This class of graphs has been studied extensively and generalized in many different directions. Induced subgraphs of the hypercube on binary s...

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Published inDiscrete Applied Mathematics Vol. 300; pp. 56 - 71
Main Authors Eğecioğlu, Ömer, Iršič, Vesna
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 15.09.2021
Elsevier BV
Subjects
Apexes
Companion stars
Cubes
Degree sequence
Fibonacci cube
Fibonacci numbers
Fibonacci-run graph
Generating function
Graph theory
Graphs
Hypercubes
Sequences
Strings
Vertex sets
Fibonacci cube
Degree sequence
Generating function
Fibonacci-run graph
Online AccessGet full text
ISSN0166-218X
1872-6771
DOI10.1016/j.dam.2021.05.018

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Abstract Fibonacci cubes are induced subgraphs of hypercube graphs obtained by restricting the vertex set to those binary strings which do not contain consecutive 1s. This class of graphs has been studied extensively and generalized in many different directions. Induced subgraphs of the hypercube on binary strings with restricted runlengths as vertices define Fibonacci-run graphs. These graphs have the same number of vertices as Fibonacci cubes, but fewer edges and different graph theoretical properties. Basic properties of Fibonacci-run graphs are presented in a companion paper, while in this paper we consider the nature of the degree sequences of Fibonacci-run graphs. The generating function we obtain is a refinement of the generating function of the degree sequences, and has a number of corollaries, obtained as specializations. We also obtain several properties of Fibonacci-run graphs viewed as a partially ordered set, and discuss its embedding properties.
AbstractList Fibonacci cubes are induced subgraphs of hypercube graphs obtained by restricting the vertex set to those binary strings which do not contain consecutive 1s. This class of graphs has been studied extensively and generalized in many different directions. Induced subgraphs of the hypercube on binary strings with restricted runlengths as vertices define Fibonacci-run graphs. These graphs have the same number of vertices as Fibonacci cubes, but fewer edges and different graph theoretical properties. Basic properties of Fibonacci-run graphs are presented in a companion paper, while in this paper we consider the nature of the degree sequences of Fibonacci-run graphs. The generating function we obtain is a refinement of the generating function of the degree sequences, and has a number of corollaries, obtained as specializations. We also obtain several properties of Fibonacci-run graphs viewed as a partially ordered set, and discuss its embedding properties.
Fibonacci cubes are induced subgraphs of hypercube graphs obtained by restricting the vertex set to those binary strings which do not contain consecutive 1s. This class of graphs has been studied extensively and generalized in many different directions. Induced subgraphs of the hypercube on binary strings with restricted runlengths as vertices define Fibonacci-run graphs. These graphs have the same number of vertices as Fibonacci cubes, but fewer edges and different graph theoretical properties. Basic properties of Fibonacci-run graphs are presented in a companion paper, while in this paper we consider the nature of the degree sequences of Fibonacci-run graphs. The generating function we obtain is a refinement of the generating function of the degree sequences, and has a number of corollaries, obtained as specializations. We also obtain several properties of Fibonacci-run graphs viewed as a partially ordered set, and discuss its embedding properties.
Author Eğecioğlu, Ömer
Iršič, Vesna
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Keywords Fibonacci cube
Degree sequence
Generating function
Fibonacci-run graph
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Snippet Fibonacci cubes are induced subgraphs of hypercube graphs obtained by restricting the vertex set to those binary strings which do not contain consecutive 1s....
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SubjectTerms Apexes
Companion stars
Cubes
Degree sequence
Fibonacci cube
Fibonacci numbers
Fibonacci-run graph
Generating function
Graph theory
Graphs
Hypercubes
Sequences
Strings
Vertex sets
Title Fibonacci-run graphs II: Degree sequences
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