The ubiquitous nature of computers with the rapid advent of technology has exponentially increased the need to secure the confidential information from misuse. Digital communications has led to the combination of both cryptography and steganography which were earlier used separately, to provide the optimum security. Steganography has the advantage of hiding the information in the cover in an invisible way such that the secret isn't visible to the naked eye. The proposed methodology implements image steganography using three keys for selecting the sub-band for embedding, selecting the order of the coefficients and deciding the number of bits to be embedded, respectively. Graph theory is made use of to select the order of the coefficients of the Integer Wavelet Transform. This present method offers good imperceptibility along with immaculate triple security with Kl, K2 and K3. © 2012 Academic Journals Inc.