Maximum and minimum Fibonacci Word Index

Determine the maximum and minimum values of the Fibonacci Word Index for trees constructed from Fibonacci words, using the Albertson index as a comparative framework.

Background

The paper defines the Fibonacci Word Index as an Albertson-index analogue for trees constructed from Fibonacci words, alongside total and modified variants. Although several inequalities are established, the extremal values of the Fibonacci Word Index itself are not determined. The stated problem asks for both the largest and smallest possible values, presumably over the relevant class of Fibonacci word trees, and proposes comparison with the classical Albertson index as a possible approach.

References

The question that should be at the centre of any research of which this research is the basis is: What is the maximum value of the Fibonacci word index and what is the minimum value of the Fibonacci word index?

— Irregularity and Topological Indices in Fibonacci Word Trees and Modified Fibonacci Word Index  (2505.00602 - Hamoud et al., 1 May 2025) in Section 4, subsection “Open questions”