Graph Theory With Applications

An introduction to graph theory. Presents the basic material, together with a wide variety of applications, both to other branches of mathematics and to real-world problems. Several good algorithms are included and their efficiencies are analysed.

**Tag(s):**
Graph Theory

**Publication date**: 31 Dec 1976

**ISBN-10**:
0333226941

**ISBN-13**:
9780333226940

**Paperback**:
270 pages

**Views**: 25,892

Graph Theory With Applications

An introduction to graph theory. Presents the basic material, together with a wide variety of applications, both to other branches of mathematics and to real-world problems. Several good algorithms are included and their efficiencies are analysed.

Terms and Conditions:

From the Preface:

This book is intended as an introduction to graph theory. Our aim has been to present what we consider to be the basic material, together with a wide variety of applications, both to other branches of mathematics and to real-world problems. Included are simple new proofs of theorems of Brooks, Chvatal, Tutte and Vizing. The applications have been carefully selected, and are treated in some depth. We have chosen to omit all so-called "applications" that employ just the language of graphs and no theory. The applications appearing at the end of each chapter actually make use of theory developed earlier in the same chapter. We have also stressed the importance of efficient methods of solving problems. Several good algorithms are included and their efficiencies are analysed. We do not, however, go into the computer implementation of these algorithms.

The exercises at the end of each section are of varying difficulty. The harder ones are starred (*) and, for these, hints are provided in appendix I. In some exercises, new definitions are introduced. The reader is recommended to acquaint himself with these definitions. Other exercises, whose numbers are indicated by bold type, are used in subsequent sections; these should all be attempted.

Appendix II consists of a table in which basic properties of four graphs are listed. When new definitions are introduced, the reader may find it helpful to check his understanding by referring to this table. Appendix III includes a selection of interesting graphs with special properties. These may prove to be useful in testing new conjectures. In appendix IV, we collect together a number of unsolved problems, some known to be very difficult, and others more hopeful. Suggestions for further reading are given in appendix V.

J. A. Bondy wrote:The text Graph Theory with Applications by U.S.R. Murty and myself has been out of print for some time. Professor Murty and I are currently preparing a new introduction to the subject, with the tentative title Graph Theory. In the meantime, we are making available pdf files of Graph Theory with Applications. They are strictly for personal use.

From the Preface:

This book is intended as an introduction to graph theory. Our aim has been to present what we consider to be the basic material, together with a wide variety of applications, both to other branches of mathematics and to real-world problems. Included are simple new proofs of theorems of Brooks, Chvatal, Tutte and Vizing. The applications have been carefully selected, and are treated in some depth. We have chosen to omit all so-called "applications" that employ just the language of graphs and no theory. The applications appearing at the end of each chapter actually make use of theory developed earlier in the same chapter. We have also stressed the importance of efficient methods of solving problems. Several good algorithms are included and their efficiencies are analysed. We do not, however, go into the computer implementation of these algorithms.

The exercises at the end of each section are of varying difficulty. The harder ones are starred (*) and, for these, hints are provided in appendix I. In some exercises, new definitions are introduced. The reader is recommended to acquaint himself with these definitions. Other exercises, whose numbers are indicated by bold type, are used in subsequent sections; these should all be attempted.

Appendix II consists of a table in which basic properties of four graphs are listed. When new definitions are introduced, the reader may find it helpful to check his understanding by referring to this table. Appendix III includes a selection of interesting graphs with special properties. These may prove to be useful in testing new conjectures. In appendix IV, we collect together a number of unsolved problems, some known to be very difficult, and others more hopeful. Suggestions for further reading are given in appendix V.

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About The Author(s)

John Adrian Bondy, (Born 1944) a dual British and Canadian citizen, was a professor of graph theory at the University of Waterloo, in Canada. He is a faculty member of Université Lyon 1, France. Bondy is known for his work on Bondy–Chvátal theorem together with Václav Chvátal. His coauthors include Paul Erdős. Bondy received his Ph.D. in graph theory from University of Oxford in 1969. Bondy has served as a managing editor and co-editor-in-chief of the Journal of Combinatorial Theory, Series B.

Uppaluri Siva Ramachandra Murty or U. S. R. Murty (as he prefers to write his name), is a Professor Emeritus of the Department of Combinatorics and Optimization, University of Waterloo.U. S. R. Murty received his Ph.D. in 1967 from the Indian Statistical Institute, Calcutta, with a thesis on extremal graph theory. Murty is well known for his work in matroid theory and graph theory, and mainly for being a co-author with J. A. Bondy of a textbook on graph theory. Murty has served as a managing editor and co-editor-in-chief of the Journal of Combinatorial Theory, Series B.

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