Among all existing alignment-free methods for comparing biological sequences, the sequence graphical representation provides a simple approach to view, sort, and compare gene structures. The aim of graphical representation is to display DNA or protein sequences graphically so that we can easily find out visually how similar or how different they are. Of course, only the visual comparison of sequences is not enough for the follow-up research work. We need more accurate comparison. This leads us to develop the application of the graphical representation for biological sequences.In this thesis, we have two main contributions: (1) We construct a protein map with the help of our proposed new graphical representation for protein sequences. Each p...