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To us, what makes graph theory beautiful is its simplicity and depth. It is simple enough to explain to high school students, yet deep enough to draw the attention of some of the world's smartest people. The visually stunning representations of graph theory help us to understand intuitively strong theories and solve complicated problems. In this book, we have used partially ordered relations as the source tool for developing a model for safe communication of a DNA sequence. The visual representation of graphs is used as a key for safe transfer. We trust that this book would be of interest to anyone who enjoys the beauty of graph theory.