1.Basic Terminology, Notation and Results
1.1 Sets, Matrices and Vectors
1.2 Digraphs, Subdigraphs, Neighbours, Degrees
1.3 Isomorphism and Basic Operations on Digraphs
1.4 Walks, Trails, Paths, Cycles and Path-Cycle Subdigraphs
1.5 Strong and Unilateral Connectivity
1.6 Undirected Graphs, Biorientations and Orientations
1.7 Trees and Euler Trails in Digraphs
1.8 Mixed Graphs, Orientations of Digraphs, and Hypergraphs
1.9 Depth-First Search
1.10 Exercises
2.Classes of Digraphs
2.1 Acyclic Digraphs
2.2 Multipartite Digraphs and Extended Digraphs
2.3 Transitive Digraphs, Transitive Closures and Reductions
2.4 Line Digraphs
2.5 The de Bruijn and Kantz Digraphs
2.6 Series-Parallel Digraphs
2.7 Quasi-Transitive Digraphs
2.8 Path-Mergeable Digraphs
2.9 Locally In/Out-Semicomplete Digraphs
2.10 Locally Semicomplete Digraphs
2.10.1 Round Digraphs
2.10.2 Non-Strong Locally Semicomplete Digraphs
2.10.3 Strong Round Decomposable Locally Semicomplete Digraphs
2.10.4 Classification of Locally Semicomplete Digraphs
2.11 Totally φ-Decomposable Digraphs
2.12 Planar Digraphs
2.13 Digraphs of Bounded Width
2.13.1 Digraphs of Bounded Tree-Width
2.13.2 Digraphs of Bounded Directed Widths
2.14 Other Families of Digraphs
2.14.1 Circulant Digraphs
2.14.2 Arc-Locally Semicomplete Digraphs
2.14.3 Intersection Digraphs
2.15 Exercises
3.Distances
3.1 Terminology and Notation on Distances
3.2 Structure of Shortest Paths
3.3 Algorithms for Finding Distances in Digraphs
3.3.1 Breadth-First Search (BFS)
3.3.2 Acyclic Digraphs
3.3.3 Dijkstra's Algorithm
3.3.4 The Bellman-Ford-Moore Algorithm
3.3.5 The Floyd-Warshall Algorithm
3.4 Inequalities on Diameter
3.5 Minimum Diameter of Orientations of Multigraphs
3.6 Minimum Diameter Orientations of Some Graphs and Digraphs
3.6.1 Generalizations of Tournaments
3.6.2 Extended Digraphs
3.6.3 Cartesian Products of Graphs
3.6.4 Chordal Graphs
3.7 Kings in Digraphs
3.7.1 2-Kings in Tournaments
3.7.2 Kings in Semicomplete Multipartite Digraphs
3.7.3 Kings in Generalizations of Tournaments
3.8 (k, l)-Kernels
3.8.1 Kernels
3.8.2 Quasi-Kernels
3.9 Exercises
4.Flows in Networks
4.1 Definitions and Basic Properties
4.1.1 Flows and Their Balance Vectors
4.1.2 The Residual Network
4.2 Reductions Among Different Flow Models
4.2.1 Eliminating Lower Bounds
4.2.2 Flows with One Source and One Sink
4.2.3 Circulations
4.2.4 Networks with Bounds and Costs on the Vertices
4.3 Flow Decompositions
4.4 Working with the Residual Network
4.5 The Maximum Flow Problem
4.5.1 The Ford-Fulkerson Algorithm
4.5.2 Maximum Flows and Linear Programming
4.6 Polynomial Algorithms for Finding a Maximum (s, t)-Flow
……
