# Luka Podrug: Horadam cubes

Date of publication: 19. 1. 2024

Discrete mathematics seminar

Monday

22

January

Time:

12:15

Location:

Predavalnica 3.07 (Jadranska 21)

**Abstract**. In this seminar, we define a new three-parameter family of graphs which further generalizes the Fibonacci and metallic cubes. Namely, the number of vertices in this family of graphs satisfies Horadam recurrence, a linear recurrence of order two. We present that many appealing and useful properties of the Fibonacci and metallic cubes are preserved. In particular, we present recursive decomposition and decomposition into grids, explore some metric and enumerative properties such as number of the edges, distribution of the degrees and cube polynomials. We also answer the question on the existence of the Hamiltonian paths and cycles.

**Note the change of time and place from our regular seminar sesions**