Let
be the circulant graph
with
and let
be its edge ideal in the ring
. Under the hypothesis that
is prime we : 1) compute the regularity index of
; 2) compute the Castelnuovo-Mumford regularity when
is Cohen-Macaulay; 3) prove that the circulant graphs with
are sequentially
.
We end characterizing the Cohen-Macaulay circulant graphs of Krull dimension
and computing their Cohen-Macaulay type and Castelnuovo-Mumford regularity.