Spectral multiplicity functions of adjacency operators of graphs and cospectral infinite graphs
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...
Saved in:
| Date: | 2024 |
|---|---|
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2024
|
| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2224 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| id |
oai:ojs.admjournal.luguniv.edu.ua:article-2224 |
|---|---|
| record_format |
ojs |
| spelling |
oai:ojs.admjournal.luguniv.edu.ua:article-22242024-04-21T17:47:57Z Spectral multiplicity functions of adjacency operators of graphs and cospectral infinite graphs de la Harpe, Pierre spectral graph theory, adjacency operator, spectral measure, spectral multiplicity function, unitarily equivalent operators, cospectral graphs, Jacobi matrix 05C50, 47A10 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 also explicit examples of infinite connected graphs which are uniquely determined by their spectrum. Lugansk National Taras Shevchenko University The author acknowledges support of the Swiss NSF grant 200020-20040. 2024-04-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2224 10.12958/adm2224 Algebra and Discrete Mathematics; Vol 37, No 1 (2024) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2224/pdf Copyright (c) 2024 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
spectral graph theory adjacency operator spectral measure spectral multiplicity function unitarily equivalent operators cospectral graphs Jacobi matrix 05C50 47A10 |
| spellingShingle |
spectral graph theory adjacency operator spectral measure spectral multiplicity function unitarily equivalent operators cospectral graphs Jacobi matrix 05C50 47A10 de la Harpe, Pierre Spectral multiplicity functions of adjacency operators of graphs and cospectral infinite graphs |
| topic_facet |
spectral graph theory adjacency operator spectral measure spectral multiplicity function unitarily equivalent operators cospectral graphs Jacobi matrix 05C50 47A10 |
| format |
Article |
| author |
de la Harpe, Pierre |
| author_facet |
de la Harpe, Pierre |
| author_sort |
de la Harpe, Pierre |
| title |
Spectral multiplicity functions of adjacency operators of graphs and cospectral infinite graphs |
| title_short |
Spectral multiplicity functions of adjacency operators of graphs and cospectral infinite graphs |
| title_full |
Spectral multiplicity functions of adjacency operators of graphs and cospectral infinite graphs |
| title_fullStr |
Spectral multiplicity functions of adjacency operators of graphs and cospectral infinite graphs |
| title_full_unstemmed |
Spectral multiplicity functions of adjacency operators of graphs and cospectral infinite graphs |
| title_sort |
spectral multiplicity functions of adjacency operators of graphs and cospectral infinite graphs |
| description |
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 also explicit examples of infinite connected graphs which are uniquely determined by their spectrum. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2024 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2224 |
| work_keys_str_mv |
AT delaharpepierre spectralmultiplicityfunctionsofadjacencyoperatorsofgraphsandcospectralinfinitegraphs |
| first_indexed |
2024-04-21T19:20:17Z |
| last_indexed |
2024-04-21T19:20:17Z |
| _version_ |
1803076172466094080 |