Graph theory is an important field of Mathematics and Computer Science. Graphs are useful Mathematical tools for modeling the relationships among objects, which are represented by vertices. In their turn, relationships between vertices are represented by edges. In this context, graph theory received considerable attention, not only from the mathematical community, but also from the whole scientific community. Coloring and Labeling find applications in scheduling problems. Embedding problems play a vital role in modifying algorithms. Over the years, there have been a large number of significant and authoritative graph contributions in Biochemistry, Computer Science, Genetics, Cheminformatics and in Sociology. Recently, graph theoretical concepts are being widely used to study and model various computer applications such as image segmentation, information retrieval, networking, clustering, etc.,