Background/Objectives: The advancement of information exchange through internet has made it easy to transfer the exact information faster to the destination. Exchange the information safely to the destination with no alterations, there are many approaches like Cryptography, Steganography and Watermarking. Methods/Statistical Analysis: Steganography is a method of hiding a secret data in other cover medium. Digital Images are popular for cover medium than other because of their frequent use on the internet. In this paper a transform domain steganography with 9/7 Integer Wavelet Transform [IWT) is proposed. A pixel adaptive embedding method using LSB [Least Significant Bit) method is employed to increase the security of the secret data embedded in the a cover medium. Graph Theory is used to select the coefficients randomly for embedding the secret messages. Findings: It is found that the proposed method provides good security and high capacity. This algorithm can be applicable for all kinds of secret communications. Finally Results are compared with 5/3 IWT. Applications/Improvements: This method can be applied for all the secret communication applications especially Defence, Telemedicine, etc. This proposed method developed further in terms of robust against various steganalysis tools.