Spectral Generalizations of Line Graphs

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.

• First book to give a detailed treatment of graph angles, star partitions and associated techniques
• Over 300 references from a broad range of sources
• Introductory chapter motivates investigation of eigenspaces by surveying in detail the limitations of eigenvalues alone