Spectral Graph Theory on Pre Fractals

Abstract

Graph Theory and Linear Algebra are two important fields of mathematics and spectral graph theory lies in their intersection. This theory involves investigations of the relationship of the usual topological properties of a graph with the spectral properties of various matrices associated with it, which is large field with many important results. Most of the work in this field has been descriptive and determined. The subject has its genesis with paper by L. Collatz and U. Sinogowitz. Since that time the subject has steadily grown and has shown surprising relationships with other mathematical areas.