Graph Theory Book 1.0 r1843

The Graph Theory Book is a comprehensive book on algorithmic graph theory signed by David Joyner, Minh Van Nguyen, and Nathann Cohen.

The Graph Theory Book is an introductory book on algorithmic graph theory. Theory and algorithms are illustrated using the Sage open source mathematics software.

Here are some key features of "Graph Theory Book":

· Introduction to Graph Theory
· Graphs and digraphs
· Subgraphs and other graph types
· Representing graphs as matrices
· Isomorphic graphs
· New graphs from old
· Common applications
· Application: finite automata

Graph algorithms:
· Representing graphs in a computer
· Graph searching
· Weights and distances
· Dijkstra`s algorithm
· Bellman-Ford algorithm
· Floyd-Roy-Warshall algorithm
· Johnson`s algorithm
· Trees and Forests
· Definitions and examples
· Properties of trees
· Minimum spanning trees
· Binary trees
· Huffman codes
· Tree traversals
· Tree Data Structures
· Priority queues
· Binary heaps
· Binomial heaps
· Binary search trees
· AVL trees
· Distance and Connectivity
· Paths and distance
· Vertex and edge connectivity
· Ford-Fulkerson theorem
· Menger???s Theorem
· Whitney???s Theorem
· Centrality of a vertex
· Network reliability
· Optimal Graph Traversals
· Eulerian graphs
· Hamiltonian graphs
· The Chinese Postman Problem
· The Traveling Salesman Problem

Planar Graphs:
· Planarity and Euler`s Formula
· Kuratowski`s Theorem
· Planarity algorithms

· Graph Coloring
· Vertex coloring
· Edge coloring
· Applications of graph coloring

· Network Flows
· Flows and cuts
· Ford and Fulkerson`s theorem
· Edmonds and Karp`s algorithm
· Goldberg and Tarjan`s algorithm

· Random Graphs
· Network statistics
· Binomial random graph model
· Erdos-Renyi model
· Small-world networks
· Scale-free networks

Graph problems and their LP Formulations:
· Maximum average degree
· Traveling Salesman Problem
· Edge-disjoint spanning trees
· Steiner tree
· Linear arboricity
· Acyclic edge coloring
· H-minor