Giancarlo Rinaldo: Some algebraic invariants of edge ideal of circulant graphs, 95-105

Abstract:

Let $ G$ be the circulant graph $ C_n(S)$ with $ S\subseteq\{ 1,\ldots,\left \lfloor\frac{n}{2}\right \rfloor\}$ and let $ I(G)$ be its edge ideal in the ring $ K[x_0,\ldots,x_{n-1}]$. Under the hypothesis that $ n$ is prime we : 1) compute the regularity index of $ R/I(G)$; 2) compute the Castelnuovo-Mumford regularity when $ R/I(G)$ is Cohen-Macaulay; 3) prove that the circulant graphs with $ S=\{1,\ldots,s\}$ are sequentially $ S_2$ . We end characterizing the Cohen-Macaulay circulant graphs of Krull dimension $ 2$ and computing their Cohen-Macaulay type and Castelnuovo-Mumford regularity.

Key Words: Circulant graphs, Cohen-Macaulay, Serre's condition.

2010 Mathematics Subject Classification: Primary 13F55. Secondary 13H10

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