# Optimal cube factors of Fibonacci and matchable Lucas cubes

## TL;DR

This paper introduces the concept of optimal cube factors in graphs and investigates their properties specifically in Fibonacci and matchable Lucas cubes, linking these findings to Padovan sequences and binomial coefficients.

## Contribution

It is the first to study optimal cube factors in Fibonacci and matchable Lucas cubes, providing new insights and results related to these graph classes.

## Key findings

- Derived results connecting optimal cube factors to Padovan sequence
- Established relationships between cube factors and binomial coefficients
- Provided new bounds or formulas for the cube factors of specific graph families

## Abstract

The optimal cube factor of a graph, a special kind of component factor, is first introduced. Furthermore, the optimal cube factors of Fibonacci and matchable Lucas cubes are studied; and some results on the Padovan sequence and binomial coefficients are obtained.