Recent results in the theory of graph spectra. (English) Zbl 0634.05054

Cvetković, Dragos M.; Doob, Michael; Gutman, Ivan; Torgašev, Aleksandar

Annals of Discrete Mathematics, 36. Amsterdam etc.: North-Holland. XI, 306 p.; $ 97.25; Dfl. 185.00 (1988).

This book is an extensive survey of the development of the theory of graph spectra between 1978 an 1984. (An essentially complete account of the older theory is in a book by the first two authors and H. Sachs, Spectra of Graphs - Theory and application, Academic Press, New York (1980; Zbl 0458.05042).) The present book quotes 213 theorems from over 700 references and places them in context with other results. Usually, proofs are given only when they are short. A list of all graphs with 7 vertices and their spectra complements the tables of spectra in the book quoted. The main development occurred in the following areas, each covered in a separate chapter: Spectral characterizations, strongly regular and distance-regular graphs, graph polynomials, spectra of infinite graphs. A further chapter is devoted to miscellanous results, and one chapter discusses applications to chemistry.

Reviewer: A.Neumaier

MSC:

05C50	Graphs and linear algebra (matrices, eigenvalues, etc.)
05-02	Research exposition (monographs, survey articles) pertaining to combinatorics

Keywords:

graph spectra; least eigenvalue; random graphs; matching polyomial; Hückel molecular orbital theory; strongly regular graphs; distance- regular graphs; graph polynomials; spectra of infinite graphs; chemistry