Spectral Generalizations of Line Graphs

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

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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.show more

Product details

  • Electronic book text
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • 47 b/w illus. 9 tables
  • 1139239252
  • 9781139239257

Review quote

'... 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 Societyshow more

Table of contents

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