  In the present paper, we give the exact formula for the average hitting time
(HT, as an abbreviation) of random walks from one vertex to any other vertex on
the weighted Cayley graph Cay($Z_{2n},\{\pm1\}$). Furthermore, we also give the
exact formula for the HT's of random walks on the weighted Cayley graph
Cay($Z_N,\{+1,+2\}$).
