Etude de spectre de graphe de Cayley

Abstract

· The regularity of a directed graph provides us with an eigenvalue that turns out to be the largest in magnitude for such a graph; · We will also define the notion of a path in a graph to study its connectivity; · The most interesting point in this work is the concept of the adjacency matrix of a finite regular graph, which will allow us to explore the relationship between the graph's connectivity and the eigenvalues of the matrix; · We will conclude this work with a method for calculating the eigenvalues of Cayley graphs defined from abelian groups. To this end, we will recall some results from representation theory.