In this work we propose a scheme that could be used as an alternative to the existing proof of work(PoW) scheme for mining in Bitcoin P2P network. Our scheme ensures that the miner must do at least a non-trivial amount of computation for solving the computational problem put forth in the paper and thus solving a PoW puzzle. Here, we have proposed to use the problem of finding the largest clique in a big graph as a replacement for the existing Bitcoin PoW scheme. In this paper, we have dealt with a graph having O(230) vertices and O(248) edges which is constructed deterministically using the set of transactions executed within a certain time slot. We have discussed some algorithms that can be used by any Bitcoin miner to solve the PoW puzzle. Then we discuss an algorithm that could perform this task by doing O(280) hash calculations. We have also proposed an improvement to this algorithm by which the PoW puzzle can be solved by calculating O(270.5) hashes and using O(248) space. This scheme is better than the existing proof of work schemes that use Hashcash, where a lucky miner could manage to find a solution to the proof of work puzzle by doing smaller amount of computation though it happens with very low probability. Bitcoin incentivizes the computing power of miners and hence, it is desirable that miners with more computing power always wins. Also, the Bitcoin PoW scheme only incentivizes computing power of miners but our PoW scheme incentivizes both computing power and memory of a miner. In our proposed scheme only the miner cannot randomly find a largest clique without knowing the clique number of the graph.