Security is the matter of great importance when the confidential/important information is stored and transferred across the insecure channel such as an internet where the possibility of protection of information is at high risk. Cryptography is a powerful tool to ensure the secure communication between different operators by transferring the protected information and only the authorized receiver can access the information. Though there are many encryption algorithms available in literature, the requirement of new encryption algorithms also receives importance to prevent any traditional opportunity to sniff data. In this paper, we have proposed a new algorithm to encrypt and decrypt information of interest, using graph theoretical approach.