Title: Some algebraic invariants of edge ideal of circulant graphs,
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.