Some new results about Fibonacci p-cubes

2025/02/11 by Mollard, Michel
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.07520

Abstract

The Fibonacci cube Γ_n is the subgraph of the hypercube Q_n induced by vertices with no consecutive 1s. Recently Jianxin Wei and Yujun Yang introduced a one parameter generalization, Fibonacci p-cubes Γ_n^p, which are subgraphs of hypercubes induced by strings where there is at least p consecutive 0s between two 1s. In this paper we first prove the expression conjectured by the authors for the cube polynomial of Γ_n^p. By a totally different method we then determine a generalization, the distance cube polynomial. We also complete the invariants investigated in the original paper by two new ones, the Mostar index Mo(Γ_n^p) and the Irregularity \irr(Γ_n^p).

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