The characteristic ideal of a finite, connected, regular graph
| dc.creator | Brunat, Josep M. | |
| dc.creator | Montes, Antonio | |
| dc.date | 2006-01-30 | |
| dc.date.accessioned | 2026-07-07T06:59:29Z | |
| dc.date.available | 2026-07-07T06:59:29Z | |
| dc.description | Let $Φ(x,y)\in\mathbb{C}[x,y]$ be a symmetric polynomial of partial degree $d$. The graph $G(Φ)$ is defined by taking $\mathbb{C}$ as set of vertices and the points of $\mathbb{V}(Φ(x,y))$ as edges. We study the following problem: given a finite, connected, $d$-regular graph $H$, find the polynomials $Φ(x,y)$ such that $G(Φ)$ has some connected component isomorphic to $H$ and, in this case, if $G(Φ)$ has (almost) all components isomorphic to $H$. The problem is solved by associating to $H$ a characteristic ideal which offers a new perspective to the conjecture formulated in a previous paper, and allows to reduce its scope. In the second part, we determine the characteristic ideal for cycles of lengths $\le 5$ and for complete graphs of order $\le 6$. This results provide new evidence for the conjecture. | |
| dc.description | 14 pages, see also http://www-ma2.upc.edu/~montes/ | |
| dc.identifier | https://arxiv.org/abs/math/0601733 | |
| dc.identifier | http://arxiv.org/abs/math/0601733 | |
| dc.identifier | Proc. ISSAC-2004, ACM, 50-57 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107763 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Combinatorics | |
| dc.subject | 05C75; 14H99; 14H05 | |
| dc.title | The characteristic ideal of a finite, connected, regular graph | |
| dc.type | text |