- Basic Definitions and Graph Families (§§ 1.1 - 1.2)
- Subgraphs and Graph Operations (§§ 2.1 - 2.2)
- Graph Isomorphism and Matrix Representations (§§ 2.3 - 2.5)
- Trees (§§ 3.1 - 3.3)
- Counting, Traversing and Searching Binary Trees (§§ 3.4 - 3.6)
- Depth-First and Breadth-First Search (§§ 4.1 - 4.3)
- Spanning Trees (§§ 4.4 - 4.5)
- Connectivity (§§ 5.1 - 5.3)
- Optimal Graph Traversals (§§ 6.1 - 6.4)
- Graph Colorings (§§ 10.1 - 10.2)
- Network Flows and Applications (§§ 12.1 - 12.4)

The following set of lecture notes are those for an earlier version of this course. They follow the text, *Applied Combinatorics* by Fred Roberts. They are included here as supplementary material.

- Permutations and Combinations
- Computational Complexity and Algorithms
- Fundamental Concepts - Graphs and Digraphs
- Connectedness
- Graph Coloring
- Chromatic Polynomials
- Trees
- Searching and Sorting Problems and Representing Graphs
- Depth-First Search and One-Way Street Problem
- Eulerian Chains and Paths
- Applications of Eulerian Chains and Paths
- Hamiltonian Chains and Paths and Applications
- Bipartite Matching, SDR's and Perfect Matchings
- Maximum Matchings and Minimum Covers
- Finding Maximum Matchings
- Minimum Spanning Trees
- The Shortest Route Problem
- Network Flows