Fundamental Concepts. Applications on Graph Isomorphisms. Distance and Diameter. Trees. Eulerian Graphs and Digraphs. Matchings and Factors. Connectivity. Graph Coloring. Hamiltonian Cycles. Planar Graphs. Optimal k-Fault-Tolerant Hamiltonian Graphs. Optimal 1-Fault-Tolerant Hamiltonian Graphs. Optimal k-Fault-Tolerant Hamiltonian-Laceable Graphs. Spanning Connectivity. Cubic 3*-Connected Graphs and Cubic 3*-Laceable Graphs. Spanning Diameter. Pancyclic and Panconnected Property. Mutually Independent Hamiltonian Cycles. Mutually Independent Hamiltonian Paths. Topological Properties of Butterfly Graphs. Diagnosis of Multiprocessor Systems. References. Index.