Cube Polynomial of Fibonacci and Lucas Cubes

Sandi Klavžar, Michel Mollard
2011 Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications  
The cube polynomial of a graph is the counting polynomial for the number of induced k-dimensional hypercubes (k ≥ 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
more » ... ents sequences of cube polynomials of Fibonacci and Lucas cubes are unimodal.
doi:10.1007/s10440-011-9652-4 fatcat:2c4kow6xkjg7zmt3ekvhaojrqq