A Seminar on Graph Theory

by Frank Harary (Editor)

Overview

Presented in 1962–63 by experts at University College, London, these lectures offer a variety of perspectives on graph theory. Although the opening chapters form a coherent body of graph theoretic concepts, this volume is not a text on the subject but rather an introduction to the extensive literature of graph theory. The seminar's topics are geared toward advanced undergraduate students of mathematics.
Lectures by this volume's editor, Frank Harary, include "Some Theorems and Concepts of Graph Theory," "Topological Concepts in Graph Theory," "Graphical Reconstruction," and other introductory talks. A series of invited lectures follows, featuring presentations by other authorities on the faculty of University College as well as visiting scholars. These include "Extremal Problems in Graph Theory" by Paul Erdös, "Complete Bipartite Graphs: Decomposition into Planar Subgraphs," by Lowell W. Beineke, "Graphs and Composite Games," by Cedric A. B. Smith, and several others.

Product Details

ISBN-13:	9780486805146
Publisher:	Dover Publications
Publication date:	04/20/2015
Series:	Dover Books on Mathematics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	128
File size:	6 MB

About the Author

Frank Harary (1921–2005) was a prominent American mathematician and expert on graph theory, about which he wrote several books. He taught at the University of Michigan from 1948 to 1986 and was later Distinguished Professor Emeritus at New Mexico State University at Las Cruces.

Table of Contents

Preface v

Lectures Frank Harary

1 Some Theorems and Concepts of Graph Theory 1

2 Topological Concepts in Graph Theory 13

3 Graphical Reconstruction 18

4 A Proof of Pólya's Theorem 21

5 Applications of Pólya's Theorem to Permutation Groups 25

6 Enumeration of Graphs and Digraphs 34

Invited Lectures

7 Complete Bipartite Graphs: Decomposition into Planar Subgraphs Lowell W. Beineke 42

8 Exteremal Problems in Graph Theory Paul Erdös 54

9 Applications of Probabilistic Methods to Graph Theory Paul Erdös 60

10 The Minimal Regular Graph Containing a Given Graph Paul Erdös Paul Kelly 65

11 Various Proofs of Cayley's Formula for Counting Trees J. W. Moon 70

12 On Well-Quasi-ordering Trees C. St. J. A. Nash-Williams 79

13 Universal Graphs Richard Rado 83

14 Graphs and Composite Games Cedric A. B. Smith 86

Index 113