Graph Theory and Its Applications 2e (Textbooks in Mathematics) - GROSS, JONATHAN

Graph Theory and Its Applications 2e (Textbooks in Mathematics)


Yayınevi: CRC

Yayın tarihi: 09/2005

ISBN: 9781584885054

Yazar : Jay Yellen

Ciltli | İngilizce | 800 Sayfa | Büyük boy  |  17,53x25,65x4,83 cm.

Tür: Bilgisayar / Tasarım & Masaüstü Yayıncılık  |  Matematik-İstatistik

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Offers a comprehensive but accessible, applications-driven treatment of graph theory suitable for a variety of graduate and advanced undergraduate courses Provides better coverage of algorithms and algebraic and topological graph theory than any other text Supplies hundreds of drawings that promote spatial intuition Incorporates several levels of carefully designed exercises that promote students' retention and develop and sharpen their problem-solving skills


Already an international bestseller, with the release of this greatly enhanced second edition, Graph Theory and Its Applications is now an even better choice as a textbook for a variety of courses -- a textbook that will continue to serve your students as a reference for years to come.

The superior explanations, broad coverage, and abundance of illustrations and exercises that positioned this as the premier graph theory text remain, but are now augmented by a broad range of improvements. Nearly 200 pages have been added for this edition, including nine new sections and hundreds of new exercises, mostly non-routine. 

What else is new?

New chapters on measurement and analytic graph theory 
Supplementary exercises in each chapter - ideal for reinforcing, reviewing, and testing.
Solutions and hints, often illustrated with figures, to selected exercises - nearly 50 pages worth
Reorganization and extensive revisions in more than half of the existing chapters for smoother flow of the exposition
Foreshadowing - the first three chapters now preview a number of concepts, mostly via the exercises, to pique the interest of reader

Gross and Yellen take a comprehensive approach to graph theory that integrates careful exposition of classical developments with emerging methods, models, and practical needs. Their unparalleled treatment provides a text ideal for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology.

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 Graph Isomorphism Revised! Automorphisms and Symmetry Moved and revised! Subgraphs Some Graph Operations Tests for Non-Isomorphism Matrix Representation More Graph Operations TREES Reorganized and revised! Characterizations 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: Prüfer Encoding Counting Binary Trees: Catalan Recursion SPANNING TREES Reorganized and revised! Tree-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 CONNECTIVITY Revised! Vertex- and Edge-Connectivity Constructing Reliable Networks Max-Min Duality and Menger's Theorems Block Decompositions OPTIMAL GRAPH TRAVERSALS Eulerian Trails and Tours DeBruijn Sequences and Postman Problems Hamiltonian Paths and Cycles Gray Codes and Traveling Salesman Problems PLANARITY AND KURATOWSKI'S THEOREM Reorganized and revised! Planar Drawings and Some Basic Surfaces Subdivision and Homeomorphism Extending Planar Drawings Kuratowski's Theorem Algebraic Tests for Planarity Planarity Algorithm Crossing Numbers and Thickness DRAWING GRAPHS AND MAPS Reorganized and revised! The Topology of Low Dimensions Higher-Order Surfaces Mathematical Model for Drawing Graphs Regular Maps on a Sphere Imbeddings on Higher-Order Surfaces Geometric Drawings of Graphs New! GRAPH COLORINGS Vertex-Colorings Map-Colorings Edge-Colorings Factorization New! MEASUREMENT AND MAPPINGS New Chapter! Distance in Graphs New! Domination in Graphs New! Bandwidth New! Intersection Graphs New! Linear Graph Mappings Moved and revised! Modeling Network Emulation Moved and revised! ANALYTIC GRAPH THEORY New Chapter! Ramsey Graph Theory New! Extremal Graph Theory New! Random Graphs New! SPECIAL DIGRAPH MODELS Reorganized and revised! Directed Paths and Mutual Reachability Digraphs as Models for Relations Tournaments Project Scheduling and Critical Paths Finding the Strong Components of a Digraph NETWORK FLOWS AND APPLICATIONS Flows and Cuts in Networks Solving the Maximum-Flow Problem Flows and Connectivity Matchings, Transversals, and Vertex Covers GRAPHICAL ENUMERATION Reorganized and revised! Automorphisms of Simple Graphs Graph Colorings and Symmetry Burnside's Lemma Cycle-Index Polynomial of a Permutation Group More Counting, Including Simple Graphs Polya-Burnside Enumeration ALGEBRAIC SPECIFICATION OF GRAPHS Cyclic Voltages Cayley Graphs and Regular Voltages Permutation Voltages Symmetric Graphs and Parallel Architectures Interconnection-Network Performance NON-PLANAR LAYOUTS Reorganized and revised! Representing Imbeddings by Rotations Genus Distribution of a Graph Voltage-Graph Specification of Graph Layouts Non KVL Imbedded Voltage Graphs Heawood Map-Coloring Problem APPENDIX Logic Fundamentals Relations and Functions Some Basic Combinatorics Algebraic Structures Algorithmic Complexity Supplementary Reading BIBLIOGRAPHY General Reading References SOLUTIONS AND HINTS New! INDEXES Index of Applications Index of Algorithms Index of Notations General Index

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