Front coverTitle pageDate-linePrefaceStudy GuideContents1 Introduction1.1 Graphs, Digraphs and Networks1.2 Classifying Problems1.3 Seeking Solutions

2 Graphs2.1 Graphs and Subgraphs2.2 Vertex Degrees2.3 Paths and Cycles2.4 Regular and Bipartite Graphs2.5 Case StudiesFour Cubes ProblemSocial Netzvorks

Exercises 2

3 Eulerian and Hamiltonian Graphs3.1 Exploring and Travelling3.2 Eulerian Graphs3.3 Hamiltonian Graphs3.4 Case StudiesDominoesDiagram-Tracing PuzzlesKnight's Tour ProblemGray Codes

Exercises 3

4 Digraphs4.1 Digraphs and Subdigraphs4.2 Vertex Degrees4.3 Paths and Cycles4.4 Eulerian and Hamiltonian Digraphs4.5 Case StudiesEcologySocial NetworksRotating Drum ProblemRanking in Tournaments

Exercises 4

5 Matrix Representations5.1 Adjacency Matrices5.2 Walks in Graphs and Digraphs5.3 Incidence Matrices5.4 Case StudiesInterval GraphsMarkov Chains

Exercises 5

6 Tree Structures6.1 Mathematical Properties of Trees6.2 Spanning Trees6.3 Rooted Trees6.4 Case StudyBraced Rectangular Frameworks

Exercises 6

7 Counting Trees7.1 Counting Labelled Trees7.2 Counting Binary Trees7.3 Counting Chemical TreesExercises 7

8 Greedy Algorithms8.1 Minimum Connector Problem8.2 Travelling Salesman ProblemExercises 8

9 Path Algorithms9.1 Fleury's Algorithm9.2 Shortest Path Algorithm9.3 Case StudyChinese Postman Problem

Exercises 9

10 Paths and Connectivity10.1 Connected Graphs and Digraphs10.2 Menger's Theorem for Graphs10.3 Some Analogues of Menger's Theorem10.4 Case StudyReliable Telecommunication Networks

Exercises 10

11 Planarity11.1 Planar Graphs11.2 Euler's Formula11.3 Cycle Method for Planarity Testing11.4 Kuratowski's Theorem11.5 Duality11.6 Convex PolyhedraExercises 11

12 Vertex Colourings and Decompositions12.1 Vertex Colourings12.2 Algorithm for Vertex Colouring12.3 Vertex DecompositionsExercises 12

13 Edge Colourings and Decompositions13.1 Edge Colourings13.2 Algorithm for Edge Colouring13.3 Edge DecompositionsExercises 13

14 Conclusion14.1 Classification of Problems14.2 Efficiency of Algorithms14.3 Another Classification of Problems

Suggestions for Further ReadingAppendix: Methods of ProofComputing NotesSolutions to Computer ActivitiesSolutions to Problems in the TextIndexBack Cover