Throughout the hundreds of years, the craft of planning conventions and measures have been created to manage the issues of data security. There are various applications of Graph Theory in about every field. Its major contribution is in the field of Cryptography. The need of secure communication of messages is nothing new. It has been present since ages. Ciphers can be replaced by graphs for secret communication. The complexity of graph algorithms makes it hard for the eavesdroppers to decrypt the encrypted message. An algorithm has been proposed in this paper to decide if a graph is an Euler graph. The message will be encrypted into an Euler Graph by the proposed encryption technique. An Hamiltonian circuit will be traced out from the encrypted graph. Apart from that another algorithm has been proposed for encrypting a text message with Euler Graph and the Hamiltonian circuit as the key. The complexity and the uncertainty of the decryption and interpretation of the actual message is very high and difficult as each graph carries a single character of the message. This ensures the safety of the proposed algorithm. © 2016, International Journal of Pharmacy and Technology. All rights reserved.