*(English)*Zbl 0824.05046

This is the third, enlarged edition of the book in which the second edition is reproduced and extended by two appendices surveying the recent development in the theory of graph spectra and their applications. The appendices fill up additional 58 pages, while the new references occupy 21 pages. The first edition of the book [Academic Press, New York, 1980, and Deutscher Verlag der Wissenschaften, Berlin (1980; Zbl 0458.05042)] covered almost all results about the spectra of graphs up to 1979. Later discoveries of several important applications of graph eigenvalues in combinatorics and graph theory made the book partially out of date. By surveying these new achievements in the appendices, the authors cover this gap and assure that the book will remain a valuable reference for the researchers in the field.

However, those working in combinatorics, graph theory, or the design of algorithms where graph eigenvalues became a substantial tool, should also consult related recent books and surveys. To mention only some of them, we refer to three excellent books by *N. Biggs* [Algebraic graph theory, Second edition, Cambridge University Press, Cambridge (1994; Zbl 0797.05032)], *A. E. Brouwer*, *A. M. Cohen* and *A. Neumaier* [Distance-regular graphs, Springer-Verlag, Berlin (1989; Zbl 0747.05073)], *C. D. Godsil* [Algebraic combinatorics, Chapman & Hall, New York (1993; Zbl 0784.05001)], and to the comprehensive survey by *B. Mohar* and *S. Poljak* in [Combinatorial and graph- theoretical problems in linear algebra, Ed. R. A. Brualdi et al., Springer-Verlag, 1993, IMA Vol. Math. Appl. 50, 107-151 (1993; Zbl 0806.90104)].

##### MSC:

05C50 | Graphs and linear algebra |

05-02 | Research monographs (combinatorics) |

05C85 | Graph algorithms (graph theory) |