The Degree Polynomial
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908353659142144 |
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| author | Brown, Jason I. George, Ian C. |
| author_facet | Brown, Jason I. George, Ian C. |
| contents | The degree polynomial of a multigraph $G$ is given by $\sum _{v \in V(G)} x^{\mbox{deg}(v)}$. We investigate here properties of the roots of such polynomials. In addition to examining the roots for some families of graphs with few and many degrees, we provide some bounds on the moduli of the roots. We also propose a region that contains all roots for multigraphs of order $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04882 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Degree Polynomial Brown, Jason I. George, Ian C. Combinatorics 05C31 The degree polynomial of a multigraph $G$ is given by $\sum _{v \in V(G)} x^{\mbox{deg}(v)}$. We investigate here properties of the roots of such polynomials. In addition to examining the roots for some families of graphs with few and many degrees, we provide some bounds on the moduli of the roots. We also propose a region that contains all roots for multigraphs of order $n$. |
| title | The Degree Polynomial |
| topic | Combinatorics 05C31 |
| url | https://arxiv.org/abs/2505.04882 |