Spectral multiplicity functions of adjacency operators of graphs and cospectral infinite graphs

• Date: 2024
• Main Author: de la Harpe, Pierre
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2024
• Subjects: spectral graph theory; adjacency operator; spectral measure; spectral multiplicity function; unitarily equivalent operators; cospectral graphs; Jacobi matrix; 05C50; 47A10
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2224
• Journal Title: Algebra and Discrete Mathematics

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...