Algebraic degree of Cayley colour graphs
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912890701742080 |
|---|---|
| author | Poddar, Sauvik |
| author_facet | Poddar, Sauvik |
| contents | The splitting field of a graph $Γ$ with respect to a square matrix $M$ associated with $Γ$, is the smallest field extension over the field of rationals $\mathbb{Q}$ that contains all the eigenvalues of $M$. The degree of the extension is called the algebraic degree of $Γ$ with respect to $M$. In this paper, we completely determine the splitting field of the adjacency matrix of the Cayley colour graph $\operatorname{Cay}(G,f)$ on a finite group $G$, associated with a class function $f:G\to\mathbb{Q}$ and compute its algebraic degree, which generalize the main results of Wu et al. Moreover, we study the relation between the algebraic integrality of two Cayley colour graphs, and deduce the fact that the algebraic degree and distance algebraic degree of a normal Cayley graph are same, generalizing a result of Zhang et al. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08634 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Algebraic degree of Cayley colour graphs Poddar, Sauvik Combinatorics 05C25, 05C50, 12F05 The splitting field of a graph $Γ$ with respect to a square matrix $M$ associated with $Γ$, is the smallest field extension over the field of rationals $\mathbb{Q}$ that contains all the eigenvalues of $M$. The degree of the extension is called the algebraic degree of $Γ$ with respect to $M$. In this paper, we completely determine the splitting field of the adjacency matrix of the Cayley colour graph $\operatorname{Cay}(G,f)$ on a finite group $G$, associated with a class function $f:G\to\mathbb{Q}$ and compute its algebraic degree, which generalize the main results of Wu et al. Moreover, we study the relation between the algebraic integrality of two Cayley colour graphs, and deduce the fact that the algebraic degree and distance algebraic degree of a normal Cayley graph are same, generalizing a result of Zhang et al. |
| title | Algebraic degree of Cayley colour graphs |
| topic | Combinatorics 05C25, 05C50, 12F05 |
| url | https://arxiv.org/abs/2602.08634 |