Abstract
For an edge ideal I(G) of a simple graph we study the
-graded Betti numbers that appear in the linear strand of the minimal free resolution of
where
is the comaximal graph of the integral modulo ring
. We show that the extremal Betti number of
is
where
is the Euler’s totient function and thereby we obtain a large class of edge ideals with even extremal Betti numbers. We find the regularity (Castelnuovo-Mumford) and the projective dimension of these ideals. Moreover, we exhibit explicit formulae that determine all the
-graded Betti numbers in the linear strand of the minimal free resolution of
for certain values of
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Disclosure statement
The authors declare that they have no competing interests.