The characteristic ideal of a finite, connected, regular graph

Details The characteristic ideal of a finite, connected, regular graph The characteristic ideal of a finite, connected, regular graph

2006-01-30

arxiv.org/abs/math/0601733v1

Proc. ISSAC-2004, ACM, 50-57

Mathematics

Commutative Algebra

14 pages, see also http://www-ma2.upc.edu/~montes/

Scientific paper

Let $\Phi(x,y)\in\mathbb{C}[x,y]$ be a symmetric polynomial of partial degree $d$. The graph $G(\Phi)$ is defined by taking $\mathbb{C}$ as set of vertices and the points of $\mathbb{V}(\Phi(x,y))$ as edges. We study the following problem: given a finite, connected, $d$-regular graph $H$, find the polynomials $\Phi(x,y)$ such that $G(\Phi)$ has some connected component isomorphic to $H$ and, in this case, if $G(\Phi)$ 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.

Affiliated with

Also associated with

No associations

Rating

The characteristic ideal of a finite, connected, regular graph does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The characteristic ideal of a finite, connected, regular graph, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The characteristic ideal of a finite, connected, regular graph will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-14435