Cohen-Macaulay Circulant Graphs
Commutative Algebra
2012-11-01 v1 Combinatorics
Abstract
Let G be the circulant graph C_n(S) with S a subset of {1,2,...,\lfloor n/2 \rfloor}, and let I(G) denote its the edge ideal in the ring R = k[x_1,...,x_n]. We consider the problem of determining when G is Cohen-Macaulay, i.e, R/I(G) is a Cohen-Macaulay ring. Because a Cohen-Macaulay graph G must be well-covered, we focus on known families of well-covered circulant graphs of the form C_n(1,2,...,d). We also characterize which cubic circulant graphs are Cohen-Macaulay. We end with the observation that even though the well-covered property is preserved under lexicographical products of graphs, this is not true of the Cohen-Macaulay property.
Cite
@article{arxiv.1210.8351,
title = {Cohen-Macaulay Circulant Graphs},
author = {Kevin N. Vander Meulen and Adam Van Tuyl and Catriona Watt},
journal= {arXiv preprint arXiv:1210.8351},
year = {2012}
}
Comments
14 pages