Jonathan L. Gross is a professor of computer science at Columbia University. His research interests include topology and graph theory.Jay Yellen is a professor of mathematics at Rollins College. His current areas of research include graph theory, combinatorics, and algorithms.Mark Anderson is also a mathematics professor at Rollins College. His research interest in graph theory centers on the topological or algebraic side.

• Introduction to Graph ModelsGraphs and Digraphs. Common Families of Graphs. Graph Modeling Applications. Walks and Distance. Paths, Cycles, and Trees. Vertex and Edge Attributes.Structure and RepresentationGraph Isomorphism. Automorphism and Symmetry. Subgraphs. Some Graph Operations. Tests for Non-Isomorphism. Matrix Representation. More Graph Operations.TreesCharacterizations and Properties of Trees. Rooted Trees, Ordered Trees, and Binary Trees. Binary-Tree Traversals. Binary-Search Trees. Huffman Trees and Optimal Prefix Codes. Priority Trees. Counting Labeled Trees. Counting Binary Trees. Spanning TreesTree Growing. Depth-First and Breadth-First Search. Minimum Spanning Trees and Shortest Paths. Applications of Depth-First Search. Cycles, Edge-Cuts, and Spanning Trees. Graphs and Vector Spaces. Matroids and the Greedy Algorithm.ConnectivityVertex and Edge-Connectivity. Constructing Reliable Networks. Max-Min Duality and Menger’s Theorems. Block Decompositions.Optimal Graph TraversalsEulerian Trails and Tours. DeBruijn Sequences and Postman Problems. Hamiltonian Paths and Cycles. Gray Codes and Traveling Salesman Problems.Planarity and Kuratowski’s TheoremPlanar Drawings and Some Basic Surfaces. Subdivision and Homeomorphism. Extending Planar Drawings. Kuratowski’s Theorem. Algebraic Tests for Planairty. Planarity Algorithm. Crossing Numbers and Thickness. Graph ColoringsVertex-Colorings. Map-Colorings. Edge-Colorings. Factorization.Special Digraph ModelsDirected Paths and Mutual Reachability. Digraphs as Models for Relations. Tournaments. Project Scheduling. Finding the Strong Components of a Digraph.Network Flows and ApplicationsFlows and Cuts in Networks. Solving the Maximum-Flow Problem. Flows and Connectivity. Matchings, Transversals, and Vertex Covers.Graph Colorings and SymmetryAutomorphisms of Simple Graphs. Equivalence Classes of Colorings.Appendix

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