Technique of information hiding wonderfully conceals a secret message inside a digital cover. More is the redundancy in a cover file much larger message can be concealed in it in such a way that it escapes any suspicion. The practice of information hiding has its own distinguished history; modern technology is only facilitating it as to how beautifully it can be used for maintaining privacy of information. There are many substitution based embedding algorithms that flips some randomly selected bits of cover with the assumption that it will be undetectable because of the noise commonly present in digital image of natural scenes. Substitution based embedding algorithms are prone to successful attacks. The study of Graph Theoretic Approach (GTA) is carried out to develop an approach to hide information in digital cover like an image, a graph or a map in sustainable way. By sustainable steganography we mean preserving statistics of cover in stego by avoiding possible distortion in the cover due to embedding of the message in it. The study is carried out to achieve the objectives to develop algorithm to hide information in a digital cover and digitally watermark digital vector map.