Let k be a positive integer. We compute depth and Stanley depth of the quotient ring of the edge ideal associated to the kth power of a path on n vertices. We show that both depth and Stanley depth have the same values and can be given in terms of k and n
Nearby in the stack
. For
n≥2k+1
, let
n≡0,k+1,k+2,…,n−1(mod(2k+1))
. Then we give values of depth and Stanley depth of the quotient ring of the edge ideal associated to the
kth
power of a cycle on
n
vertices and tight bounds otherwise, in terms of
n
and
k
. We also compute lower bounds for the Stanley depth of the edge ideals associated to the
kth
power of a path and a cycle and prove a conjecture of Herzog presented in HS for these ideals.