Applications of rational difference equations to spectral graph theory: expanded version

TL;DR

This paper explores a broad class of recurrence relations linked to matrix diagonalization, deriving closed-form solutions and properties, and applying these results to eigenvalue problems in spectral graph theory.

Contribution

It introduces a general framework for solving recurrence relations in spectral graph theory and applies it to eigenvalue analysis, providing new analytical tools.

Findings

Derived closed-form solutions for recurrence relations

Analyzed analytical properties of solutions

Applied methods to eigenvalue problems in graphs

Abstract

We study a general class of recurrence relations that appear in the application of a matrix diagonalization procedure. We find general closed formula and determine analytical properties of the solutions. We finally apply these findings in several problems involving eigenvalues of graphs.