Fibonacci-Constrained Graphs: Construction, Properties, and Computational Analysis

Abstract

We construct a class of graphs in which each vertex has a degree corresponding to a Fibonacci number, called Fibonacci-constrained graphs. These graphs provide a framework for studying graph connectivity, path enumeration, and network structure. We present a method for constructing such graphs, illustrate examples for small vertex sets, and perform computational analysis of their properties. The results demonstrate the interplay between Fibonacci constraints and standard graph metrics, providing insight into combinatorial design and applied network problems.