This paper presents the application of Path, Cycle and Complete Graph for safely transferring data in Cryptography. Path, Cycle and Complete Graph exhibiting antimagic labeling, and Path graph with even number of vertices exhibiting felicitous labeling for certain permutations of edge labels (for antimagic labeling scheme) and certain permutations of vertex labels (for felicitous labeling scheme) have been chosen, with the said permutations of vertex and edge labels being in lexicographic order. Two newly developed matrices namely Antimagic Label Matrix and Felicitous Label Matrix also have been used with these labelings in lexicographic order for this cryptographic application. Two types of methods have been developed - Method One and Method Two. In Method One, AES (Advanced Encryption Standard) is used with AES being presented with three choices for the initial key: K₁, K₂, K₃. In Method Two - five schemes (a, b, c, d, e) without using AES have been developed. Thus, numerous and complex cipher-texts can be produced using these methods resulting in an enhanced safety in data transfer.

lexicographic order, permutations, combinations, graph labeling, antimagic labeling, felicitous labeling, AES (Advanced Encryption Standard), antimagic label matrix, felicitous label matrix, path, cycle, complete graph.