Integral Laplacian graphs with a unique double Laplacian eigenvalue, II
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912454777241600 |
|---|---|
| author | Hameed, Abdul Tyaglov, Mikhail |
| author_facet | Hameed, Abdul Tyaglov, Mikhail |
| contents | The set $S_{\{i,j\}_{n}^{m}}=\{0,1,2,\ldots,m-1,m,m,m+1,\ldots,n-1,n\}\setminus\{i,j\},\quad 0<i<j\leqslant n$, is called Laplacian realizable if there exists a simple connected graph $G$ whose Laplacian spectrum is $S_{\{i,j\}_{n}^{m}}$. In this case, the graph $G$ is said to realize $S_{\{i,j\}_{n}^{m}}$. In this paper, we completely describe graphs realizing the sets $S_{\{i,j\}_{n}^{m}}$ with $m=1,2$ and determine the structure of these graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_07275 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Integral Laplacian graphs with a unique double Laplacian eigenvalue, II Hameed, Abdul Tyaglov, Mikhail Combinatorics The set $S_{\{i,j\}_{n}^{m}}=\{0,1,2,\ldots,m-1,m,m,m+1,\ldots,n-1,n\}\setminus\{i,j\},\quad 0<i<j\leqslant n$, is called Laplacian realizable if there exists a simple connected graph $G$ whose Laplacian spectrum is $S_{\{i,j\}_{n}^{m}}$. In this case, the graph $G$ is said to realize $S_{\{i,j\}_{n}^{m}}$. In this paper, we completely describe graphs realizing the sets $S_{\{i,j\}_{n}^{m}}$ with $m=1,2$ and determine the structure of these graphs. |
| title | Integral Laplacian graphs with a unique double Laplacian eigenvalue, II |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2307.07275 |