Recent Results in the Theory of Graph Spectra, Volume 36

1st Edition

Authors: D.M. Cvetkovic M. Doob I. Gutman A. Torgašev
Hardcover ISBN: 9780444703613
eBook ISBN: 9780080867762
Imprint: North Holland
Published Date: 1st January 1988
Page Count: 305
72.95 + applicable tax
43.99 + applicable tax
54.95 + applicable tax
Unavailable
Compatible Not compatible
VitalSource PC, Mac, iPhone & iPad Amazon Kindle eReader
ePub & PDF Apple & PC desktop. Mobile devices (Apple & Android) Amazon Kindle eReader
Mobi Amazon Kindle eReader Anything else

Institutional Access


Table of Contents

1. Characterizations of Graphs by their Spectra. 2. Distance-Regular and Similar Graphs. 3. Miscellaneous Results from the Theory of Graph Spectra. 4. The Matching Polynomial and Other Graph Polynomials. 5. Applications to Chemistry and Other Branches of Science. 6. Spectra of Infinite Graphs. Appendix: Spectra of Graphs with Seven Vertices. Bibliography. Bibliographic Index. Index.

Description

The purpose of this volume is to review the results in spectral graph theory which have appeared since 1978.

The problem of characterizing graphs with least eigenvalue -2 was one of the original problems of spectral graph theory. The techniques used in the investigation of this problem have continued to be useful in other contexts including forbidden subgraph techniques as well as geometric methods involving root systems. In the meantime, the particular problem giving rise to these methods has been solved almost completely. This is indicated in Chapter 1.

The study of various combinatorial objects (including distance regular and distance transitive graphs, association schemes, and block designs) have made use of eigenvalue techniques, usually as a method to show the nonexistence of objects with certain parameters. The basic method is to construct a graph which contains the structure of the combinatorial object and then to use the properties of the eigenvalues of the graph. Methods of this type are given in Chapter 2.

Several topics have been included in Chapter 3, including the relationships between the spectrum and automorphism group of a graph, the graph isomorphism and the graph reconstruction problem, spectra of random graphs, and the Shannon capacity problem. Some graph polynomials related to the characteristic polynomial are described in Chapter 4. These include the matching, distance, and permanental polynomials. Applications of the theory of graph spectra to Chemistry and other branches of science are described from a mathematical viewpoint in Chapter 5. The last chapter is devoted to the extension of the theory of graph spectra to infinite graphs.


Details

No. of pages:
305
Language:
English
Copyright:
© North Holland 1988
Published:
Imprint:
North Holland
eBook ISBN:
9780080867762
Hardcover ISBN:
9780444703613

Reviews

The purpose of this volume is to review the results in spectral graph theory which have appeared since 1978. The problem of characterizing graphs with least eigenvalue -2 was one of the original problems of spectral graph theory. The techniques used in the investigation of this problem have continued to be useful in other contexts including forbidden subgraph techniques as well as geometric methods involving root systems. In the meantime, the particular problem giving rise to these methods has been solved almost completely. This is indicated in Chapter 1. The study of various combinatorial objects (including distance regular and distance transitive graphs, association schemes, and block designs) have made use of eigenvalue techniques, usually as a method to show the nonexistence of objects with certain parameters. The basic method is to construct a graph which contains the structure of the combinatorial object and then to use the properties of the eigenvalues of the graph. Methods of this type are given in Chapter 2. Several topics have been included in Chapter 3, including the relationships between the spectrum and automorphism group of a graph, the graph isomorphism and the graph reconstruction problem, spectra of random graphs, and the Shannon capacity problem. Some graph polynomials related to the characteristic polynomial are described in Chapter 4. These include the matching, distance, and permanental polynomials. Applications of the theory of graph spectra to Chemistry and other branches of science are described from a mathematical viewpoint in Chapter 5. The last chapter is devoted to the extension of the theory of graph spectra to infinite graphs.


About the Authors

D.M. Cvetkovic Author

M. Doob Author

I. Gutman Author

A. Torgašev Author