Graphs and Applications An Introductory Approach [Paperback]

Discrete Mathematics is one of the fastest growing areas in mathematics today with an ever-increasing number of courses in schools and universities. Graphs and Applications is based on a highly successful Open University course and the authors have paid particular attention to the presentation, clarity and arrangement of the material, making it ideally suited for independent study and classroom use. Includes a large number of examples, problems and exercises.

Discrete Mathematics is one of the fastest growing areas in mathematics today with an ever-increasing number of courses in schools and universities. Graphs and Applications is based on a highly successful Open University course and the authors have paid particular attention to the presentation, clarity and arrangement of the material, making it ideally suited for independent study and classroom use. An important part of learning graph theory is problem solving; for this reason large numbers of examples, problems (with full solutions) and exercises (without solutions) are included.
1 Introduction.- 1.1 Graphs, Digraphs and Networks.- 1.2 Classifying Problems.- 1.3 Seeking Solutions.- 2 Graphs.- 2.1 Graphs and Subgraphs.- 2.2 Vertex Degrees.- 2.3 Paths and Cycles.- 2.4 Regular and Bipartite Graphs.- 2.5 Case Studies.- Four Cubes Problem.- Social Networks.- Exercises 2.- 3 Eulerian and Hamiltonian Graphs.- 3.1 Exploring and Travelling.- 3.2 Eulerian Graphs.- 3.3 Hamiltonian Graphs.- 3.4 Case Studies.- Dominoes.- Diagram-Tracing Puzzles.- Knights Tour Problem.- Gray Codes.- Exercises 3.- 4 Digraphs.- 4.1 Digraphs and Subdigraphs.- 4.2 Vertex Degrees.- 4.3 Paths and Cycles.- 4.4 Eulerian and Hamiltonian Digraphs.- 4.5 Case Studies.- Ecology.- Social Networks.- Rotating Drum Problem.- Ranking in Tournaments.- Exercises 4.- 5 Matrix Representations.- 5.1 Adjacency Matrices.- 5.2 Walks in Graphs and Digraphs.- 5.3 Incidence Matrices.- 5.4 Case Studies.- Interval Graphs.- Markov Chains.- ExerlCš