Cube Polynomial of Fibonacci and Lucas Cubes

Authors:
Sandi Klavžar;Michel Mollard
Affiliations:
Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia and Faculty of Natural Sciences and Mathematics, University of Maribor, Maribor, Slovenia;Institut Fourier, CNRS Université Joseph Fourier, St Martin d'Hères Cedex, France 38402
Venue:
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
Year:
2012

Citing 10
Cited 1

Structural and enumerative properties of the Fibonacci cubes

Discrete Mathematics
Fibonacci Cubes-A New Interconnection Topology

IEEE Transactions on Parallel and Distributed Systems
Extended Fibonacci Cubes

IEEE Transactions on Parallel and Distributed Systems
Observability of the extended Fibonacci cubes

Discrete Mathematics - Special issue: The 18th British combinatorial conference
Generatingfunctionology

Generatingfunctionology
Hamming polynomials and their partial derivatives

European Journal of Combinatorics
Fast Recognition of Fibonacci Cubes

Algorithmica
Roots of cube polynomials of median graphs

Journal of Graph Theory
Cage-amalgamation graphs, a common generalization of chordal and median graphs

European Journal of Combinatorics
Note: The Clar formulas of a benzenoid system and the resonance graph

Discrete Applied Mathematics

Note: Maximal hypercubes in Fibonacci and Lucas cubes

Discrete Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

The cube polynomial of a graph is the counting polynomial for the number of induced k-dimensional hypercubes (k驴0). We determine the cube polynomial of Fibonacci cubes and Lucas cubes, as well as the generating functions for the sequences of these cubes. Several explicit formulas for the coefficients of these polynomials are obtained, in particular they can be expressed with convolved Fibonacci numbers. Zeros of the studied cube polynomials are explicitly determined. Consequently, the coefficients sequences of cube polynomials of Fibonacci and Lucas cubes are unimodal.