Annihilating polynomial, Jordan canonical from, and generalized spectral characterizations of Eulerian graphs
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916437094825984 |
|---|---|
| author | Li, Kunyue Wang, Wei Zhang, Hao |
| author_facet | Li, Kunyue Wang, Wei Zhang, Hao |
| contents | Let $G$ be an Eulerian graph on $n$ vertices with adjacency matrix $A$ and characteristic polynomial $ϕ(x)$. We show that when $n$ is even (resp. odd), the square-root of $ϕ(x)$ (resp. $xϕ(x)$) is an annihilating polynomial of $A$, over $\mathbb{F}_2$. The result was achieved by applying the Jordan canonical form of $A$ over the algebraic closure $\bar{\mathbb{F}}_2$. Based on this, we show a family of Eulerian graphs are determined by their generalized spectrum among all Eulerian graphs, which significantly simplifies and strengthens the previous result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09833 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Annihilating polynomial, Jordan canonical from, and generalized spectral characterizations of Eulerian graphs Li, Kunyue Wang, Wei Zhang, Hao Combinatorics 05C50 Let $G$ be an Eulerian graph on $n$ vertices with adjacency matrix $A$ and characteristic polynomial $ϕ(x)$. We show that when $n$ is even (resp. odd), the square-root of $ϕ(x)$ (resp. $xϕ(x)$) is an annihilating polynomial of $A$, over $\mathbb{F}_2$. The result was achieved by applying the Jordan canonical form of $A$ over the algebraic closure $\bar{\mathbb{F}}_2$. Based on this, we show a family of Eulerian graphs are determined by their generalized spectrum among all Eulerian graphs, which significantly simplifies and strengthens the previous result. |
| title | Annihilating polynomial, Jordan canonical from, and generalized spectral characterizations of Eulerian graphs |
| topic | Combinatorics 05C50 |
| url | https://arxiv.org/abs/2410.09833 |