A Textbook of Graph Theory

I Basic Results.- 1.0 Introduction.- 1.1 Basic Concepts.- 1.2 Subgraphs.- 1.3 Degrees of Vertices.- 1.4 Paths and Connectedness.- 1.5 Automorphism of a Simple Graph.- 1.6 Line Graphs.- 1.7 Operations on Graphs.- 1.8 An Application to Chemistry.- 1.9 Miscellaneous Exercises.- Notes.- II Directed Graphs.- 2.0 Introduction.- 2.1 Basic Concepts.- 2.2 Tournaments.- 2.3 K-Partite Tournaments.- Notes.- III Connectivity.- 3.0 Introduction.- 3.1 Vertex Cuts and Edge Cuts.- 3.2 Connectivity and Edge-Connectivity.- 3.3 Blocks.- 3.4 Edge-Connectivity of a Graph.- 3.5 Menger's Theorem.- 3.6 Exercises.- Notes.- IV Trees.- 4.0 Introduction.- 4.1 Definition, Characterization, and Simple Properties.- 4.2 Centers and Centroids.- 4.3 Counting the Number of Spanning Trees.- 4.4 4.4 Cayley's Formula.- 4.5 Helly Property.- 4.6 Exercises.- Notes.- V Independent Sets and Matchings.- 5.0 Introduction.- 5.1 Vertex Independent Sets and Vertex Coverings.- 5.2 Edge-Independent Sets.- 5.3 Matchings and Factors.- 5.4 Matchings in Bipartite Graphs.- 5.5 * Perfect Matchings and the Tutte Matrix.- Notes.- VI Eulerian and Hamiltonian Graphs.- 6.0 Introduction.- 6.1 Eulerian Graphs.- 6.2 Hamiltonian Graphs.- 6.3 * Pancyclic Graphs.- 6.4 Hamilton Cycles in Line Graphs.- 6.5 2-Factorable Graphs.- 6.6 Exercises.- Notes.- VII Graph Colorings.- 7.0 Introduction.- 7.1 Vertex Colorings.- 7.2 Critical Graphs.- 7.3 Triangle-Free Graphs.- 7.4 Edge Colorings of Graphs.- 7.5 Snarks.- 7.6 Kirkman's Schoolgirls Problem.- 7.7 Chromatic Polynomials.- Notes.- VIII Planarity.- 8.0 Introduction.- 8.1 Planar and Nonplanar Graphs.- 8.2 Euler Formula and Its Consequences.- 8.3 K5 and K3,3 are Nonplanar Graphs.- 8.4 Dual of a Plane Graph.- 8.5 The Four-Color Theorem and the Heawood Five-Color Theorem.- 8.6 Kuratowski's Theorem.- 8.7 Hamiltonian Plane Graphs.- 8.8 Tait Coloring.- Notes.- IX Triangulated Graphs.- 9.0 Introduction.- 9.1 Perfect Graphs.- 9.2 Triangulated Graphs.- 9.3 Interval Graphs.- 9.4 Bipartite Graph B(G)of a Graph G.- 9.5 Circular Arc Graphs.- 9.6 Exercises.- 9.7 Phasing of Traffic Lights at a Road Junction.- Notes.- X Applications.- 10.0 Introduction.- 10.1 The Connector Problem.- 10.2 Kruskal's Algorithm.- 10.3 Prim's Algorithm.- 10.4 Shortest-Path Problems.- 10.5 Timetable Problem.- 10.6 Application to Social Psychology.- 10.7 Exercises.- Notes.- List of Symbols.- References.