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A beginner's guide to graph theory

Author: W D Wallis
Publisher: Boston : Birkhäuser, ©2007.
Edition/Format:   Print book : English : 2nd edView all editions and formats
Summary:

Concisely written, gentle introduction to graph theory suitable as a textbook or for self-studyGraph-theoretic applications from diverse fields (computer science, engineering, chemistry, management  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: W D Wallis
ISBN: 9780817644840 0817644849 9780817645809 0817645802
OCLC Number: 75926353
Description: xix, 260 pages : illustrations ; 24 cm
Contents: 1 Graphs 1 --
1.1 Sets, Binary Relations and Graphs 1 --
1.3 Degree 13 --
2 Walks, Paths and Cycles 19 --
2.2 Radius, Diameter and Eccentricity 23 --
2.3 Weighted Distance 25 --
2.4 Euler Walks 29 --
2.5 Hamilton Cycles 34 --
2.6 The Traveling Salesman Problem 39 --
3 Connectivity 43 --
3.1 Cutpoints and Bridges 43 --
3.2 Blocks 46 --
3.3 Connectivity 49 --
4 Trees 53 --
4.1 Characterizations of Trees 53 --
4.2 Spanning Trees 55 --
4.3 Minimal Spanning Trees 60 --
5 Linear Spaces Associated with Graphs 65 --
5.1 Finite Fields and Vector Spaces 65 --
5.2 The Power Set as a Vector Space 66 --
5.3 The Vector Spaces Associated with a Graph 68 --
5.4 The Cutset Subspace 70 --
5.5 Bases and Spanning Trees 72 --
6 Factorizations 77 --
6.1 Definitions; One-Factorizations 77 --
6.2 Tournament Applications of One-Factorizations 83 --
6.3 A General Existence Theorem 85 --
6.4 Graphs Without One-Factors 89 --
7 Graph Colorings 93 --
7.1 Vertex Colorings 93 --
7.2 Brooks' Theorem 97 --
7.3 Counting Vertex Colorings 99 --
7.4 Edge-Colorings 104 --
7.5 Class 2 Graphs 107 --
8 Planarity 113 --
8.1 Representations and Crossings 113 --
8.2 Euler's Formula 116 --
8.3 Maps, Graphs and Planarity 119 --
9 Labeling 123 --
9.1 Introduction; Graceful Labelings 123 --
9.2 Edge-Magic Total Labeling 126 --
9.3 Edge-Magic Labelings of Complete Graphs 132 --
10 Ramsey Theory 139 --
10.1 The Graphical Case of Ramsey's Theorem 139 --
10.2 Ramsey Multiplicity 144 --
10.3 Application of Sum-Free Sets 146 --
10.4 Bounds on Classical Ramsey Numbers 149 --
10.5 The General Case of Ramsey's Theorem 152 --
11 Digraphs 155 --
11.2 Orientations and Tournaments 159 --
11.3 Directed Euler Walks 163 --
12 Critical Paths 167 --
12.1 Activity Digraphs 167 --
12.2 Critical Path Analysis 170 --
12.3 Critical Paths Under Uncertainty 176 --
13 Flows in Networks 181 --
13.1 Transportation Networks and Flows 181 --
13.2 Maximal Flows 186 --
13.3 The Max Flow Min Cut Theorem 192 --
13.4 The Max Flow Min Cut Algorithm 193 --
13.5 Supply and Demand Problems 200 --
14 Computational Considerations 205 --
14.1 Computation Time 205 --
14.2 Data Structures 208 --
14.3 Some Graph Algorithms 209 --
14.4 Intractability 213 --
15 Communications Networks and Small-Worlds 217 --
15.2 Functions on Graphs 218 --
15.3 Classes of Graphs 220 --
15.4 Small-World Graphs 222.
Responsibility: W.D. Wallis.

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From the reviews: "Altogether the book gives a comprehensive introduction to graphs, their theory and their application...The use of the text is optimized when the exercises are solved. The obtained Read more...

 
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