The Mostar index of Fibonacci and Lucas cubes

TL;DR

This paper calculates the Mostar index, a measure of how far a graph is from being distance-balanced, for Fibonacci and Lucas cubes, contributing to the understanding of their structural properties.

Contribution

It provides the first explicit determination of the Mostar index for Fibonacci and Lucas cubes, expanding the graph invariants studied for these families.

Findings

Mostar index values for Fibonacci cubes are derived.

Mostar index values for Lucas cubes are derived.

Results enhance understanding of graph distance properties.

Abstract

The Mostar index of a graph was defined by Do\v{s}li\'{c}, Martinjak, \v{S}krekovski, Tipuri\'{c} Spu\v{z}evi\'{c} and Zubac in the context of the study of the properties of chemical graphs. It measures how far a given graph is from being distance-balanced. In this paper, we determine the Mostar index of two well-known families of graphs: Fibonacci cubes and Lucas cubes.