2023/08/08 by Pierre de la Harpe, de la Harpe, Pierre
Computer Science · Mathematics · #05C50 #47A10 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2308.04339
openalex publication_date 2023/08/08 · openalex created_date 2023/08/18 · openalex updated_date 2026/07/28
The adjacency operator of a graph has a spectrum and a class of scalar-valued spectral measures which have been systematically analyzed; it also has a spectral multiplicity function which has been less studied. The first purpose of this article is to review some examples of infinite graphs for which the spectral multiplicity function of the adjacency operator has been determined. The second purpose of this article is to show explicit examples of infinite connected graphs which are cospectral, i.e., which have unitarily equivalent adjacency operators, and explicit examples of infinite connected graphs which are uniquely determined by their spectrum.