A note on the cube polynomials of Fibonacci and Lucas-run graphs

Abstract

The cube polynomials of the Fibonacci-run graph R_n and Lucas-run graph R^l_n are determined, and a conjecture on the relation between them is proved. Note that Mollard (2025) [9] has considered deeply this question and obtained many general conclusions. Here we study this depending only on the decompositions of R_n and R^l_n.

_{Mathematics Subject Classification (2020): 05C75, 68R10.}