Because of its inherent simplicity, graph theory has a wide range of applications in engineering, and in physical sciences. It has of course uses in social sciences, in linguistics and in numerous other areas. In fact, a graph can be used to represent almost any physical situation involving discrete objects and the relationship among them. Now with the solutions to engineering and other problems becoming so complex leading to larger graphs, it is virtually difficult to analyze without the use of compute Table of Contents Preface. Introduction. Paths and Circuits. Trees and Fundamental Circuits. Cut-Sets and Cut-Vertices. Planar and Dual Graphs. Vector Spaces of a Graph. Matrix Representation of Graphs. Coloring, Covering, and Partitioning. Directed Graphs. Enumeration of Graphs. Graph Theoretic Algorithms and Computer Programs. Graphs in Switching and Coding Theory. Electrical Network Analysis by Graph Theory. Graph Theory in Operations Research. Survey of other Applications. APPENDIX A: Binet-Cauchy Theorem. APPENDIX B: Nullity of a Matrix and Sylvester's Law. Index

Introduction, Paths and circuits, etc.