Spectral Generalizations of Line Graphs
On Graphs with Least Eigenvalue -2

An important resource for all researchers with an interest in algebraic graph theory.

Dragoš Cvetkovic (Author), Peter Rowlinson (Author), Slobodan Simic (Author)

9780521836630, Cambridge University Press

Paperback, published 22 July 2004

310 pages, 47 b/w illus. 9 tables
22.8 x 15.4 x 1.7 cm, 0.416 kg

'… a wealth of detail … this class can now claim to be the best understood corner of graph theory, and this book will be the standard guide.' Bulletin of the London Mathematical Society

Line graphs have the property that their least eigenvalue is greater than or equal to –2, a property shared by generalized line graphs and a finite number of so-called exceptional graphs. This book deals with all these families of graphs in the context of their spectral properties. The authors discuss the three principal techniques that have been employed, namely 'forbidden subgraphs', 'root systems' and 'star complements'. They bring together the major results in the area, including the recent construction of all the maximal exceptional graphs. Technical descriptions of these graphs are included in the appendices, while the bibliography provides over 250 references. This will be an important resource for all researchers with an interest in algebraic graph theory.

1. Introduction
2. Forbidden subgraphs
3. Root systems
4. Regular graphs
5. Star complements
6. The Maximal exceptional graphs
7. Miscellaneous results.

Subject Areas: Combinatorics & graph theory [PBV], Algebra [PBF]