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A graph in graph theory is perhaps one representation in mathematics which is very simple but has established itself as a unique tool in contributing its applications to determine chemical, biological properties. The matrix representation of graphs has a tremendous impact in solving and simplifying numerous algorithms. This simple representation is compatible to represent DNA, RNA structures, protein sequences, protein interaction networks, molecular structures and chemical graphs. This property has enabled it to establish as a strong tool in determining physical, chemical and biological properties. On the other side, graph theory has developed as a strong tool in mathematics with numerous theoretical results and algorithms. The powerful methods found in graph theory have also been used to prove fundamental results in other areas. It is exciting and surprising to see the traces left behind by graph theory to various domains. In this book, we have used the theoretical properties of graph theory to determine chemical and biological properties. The book would be interesting for anybody interested in graph applications.