Fractional Chromatic Numbers and Chromatic Numbers for the Fibonacci Distance Graphs
Anshika Srivastava · The Fibonacci Quarterly · 2025
For a set D of positive integers, the integer distance graph G(Z,D) is a graph with vertex set Z and two vertices x and y are adjacent whenever |x−y|∈D. This paper computes the fractional chromatic number and the chromatic number of G(Z,D) when the elements of D are Fibonacci numbers defined by Fi:=Fi−1+Fi−2, i≥2 with F0=0,F1=1. In the study of chromatic numbers, we encounter an example that disproves a conjecture by Zhu [Citation12].