Graph Theory and its Applications
If you are searching for any of the following topics: Look no further. You'll find it at graph theory! Graph Theory and Its Applications is a comprehensive applications-driven textbook that provides material for several different courses. network, planar, graph, theory, discrete, Kuratowski, Euler, Hamilton, algorithm, algebra, map, isomorphism, topology, Heawood, surface, digraph, voltage graph, connectivity, spanning tree, network flow, spanning tree, binary tree, gross, yellen Topics Include: Trees, connectivity, planarity, coloring; Graphical models for electrical and communications networks and computer architectures; Network optimization models for operations analysis, including scheduling and job assignment; Voltage graphs, algebraic specification of graphs (including the wrapped butterfly), and other topics that showcase the interplay between graph theory and algebra. Features: Applications and concrete examples -- help demonstrate relevance; More than 700 graph drawings -- promote spatial intuition More than 1,600 exercises -- from routine practice to more challenging problem solving; Algorithms -- in a concise, easy-to-read format
Table of Contents INTRODUCTION to GRAPH MODELS Graphs and Digraphs Common Families of Graphs Graph Modeling Applications Walks and Distance Paths, Cycles, and Trees Vertex and Edge Attributes: More Applications STRUCTURE and REPRESENTATION Subgraphs Some Graph Operations Graph Isomorphism Tests for Non-Isomorphism Matrix Representations TREES Characterizations and Properties of Trees Rooted Trees Binary Trees Counting Binary Trees: Catalan Recursion Traversing a Binary Tree Binary-Search Trees Priority Trees SPANNING TREES An Intuitive Tree-Growing Scheme Depth-First and Breadth-First Search Applications of Depth-First Search Counting Spanning Trees: Prüfer Encoding Minimum Spanning Trees and Shortest Paths Cycles, Edge-Cuts, and Spanning Trees Graphs and Vector Spaces Matroids and the Greedy Algorithm CONNECTIVITY Vertex- and Edge-Connectivity Constructing Reliable Networks Max-Min Duality and Menger's Theorems Block Decompositions OPTIMAL GRAPH TRANSVERSALS Eulerian Trails and Tours DeBruijn Sequences and Postman Problems Hamiltonian Paths and Cycles Gray Codes and Traveling Salesman Problems GRAPH OPERATIONS and MAPPINGS Binary Operations on Graphs Linear Graph Mappings Modeling Network Emulation Subdivision and Homeomorphism Transforming a Graph by Edge Contraction DRAWING GRAPHS AND MAPS The Topology of Graphs and of the Sphere Higher-Order Surfaces Drawing Imbeddings Numerical Relations for Imbeddings Regular Sphere Maps PLANARITY OF GRAPHS Planarity and Nonplanarity Extending Planar Drawings Kuratowski's Theorem Planarity Algorithm GRAPH COLORINGS Vertex-Colorings Map-Colorings Edge-Colorings SPECIAL DIGRAPH MODELS Basic Properties and Some New Terminology Selected Applications of the General Digraph Tournaments and Project Scheduling Finding the Strong Components of a Digraph NETWORK FLOWS and APPLICATIONS Flows and Cuts in Networks Solving the Maximum-Flow Problem Determining the Connectivity of a Graph Matchings, Transversals, and Vertex Covers GRAPHICAL ENUMERATION Automorphisms and Symmetry Graph Colorings and Symmetry Cycle Index of a Permutation Group Burnside's Lemma Enumerating Vertex- and Edge-Colorings Counting Simple Graphs ALGEBRAIC SPECIFICATION of GRAPHS Cyclic Voltages Cayley Graphs and Regular Voltages Permutation Voltages Symmetric Graphs and Parallel Architectures Interconnection-Network Performance NONPLANAR LAYOUTS Crossing Numbers and Thickness Imbeddings in General Surfaces Representing Imbeddings by Rotations Genus Distribution of a Graph Voltage-Graph Specification of Graph Layouts Non-KVL Imbedded Voltage Graphs Heawood Map-Coloring Problem At graph theory, you'll discover an easy to use, information packed web site. Click here to learn more about graph theory. |
