Before revision:  In this paper, a generalized algorithm for the k-Clique problemhas been newly proposed using a classical-quantum hybrid approach , which can also be extended as a generalized algorithm for maximum clique problem . The complexity of the proposed algorithm has been reduced to O(\sqrt{2^{k*log_2n . The algorithm automatically generates the circuit for any given undirected and unweighted graph  , which makes the approach generalized in nature.
After revision:  In this paper, a generalized algorithm for the k-Clique problemhas been newly proposed using a classical-quantum hybrid approach , which can also be extended as a generalized algorithm for maximum clique problem in classical-quantum hybrid architecture . The algorithm automatically generates the circuit for any given undirected and unweighted graph , which makes the approach generalized in nature.