Some algebraic invariants of edge ideal of circulant graphs

Abstract

Let $G$ be the circulant graph $C_n(S)$ with $S\subseteq \{1,\dots ,\lfloor \frac{n}{2}\rfloor \}$ and let $I(G)$ be its edge ideal in the ring $K[x_0,\dots ,x_{n-1}]$. 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 $S=\{1,\dots ,s\}$ 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.

Cited by in corpus (3)

• 2-dimensional vertex decomposable circulant graphs
• Homological invariants of Cameron--Walker graphs
• On Gorenstein Circulant Graphs and Gorenstein SQC Graphs