be the circulant graph
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
We end characterizing the Cohen-Macaulay circulant graphs of Krull dimension
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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