Cohen–Macaulay Circulant Graphs
| Autor: | Catriona Watt, Adam Van Tuyl, Kevin N. Vander Meulen |
|---|---|
| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Communications in Algebra. 42:1896-1910 |
| ISSN: | 1532-4125 0092-7872 |
| DOI: | 10.1080/00927872.2012.749886 |
| Popis: | Let G be the circulant graph C n (S) with , and let I(G) denote 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|