Spectral Generalizations of Line Graphs

This work discusses the three major techniques for the study of line graphs and generalized line graphs, namely 'forbidden subgraphs', 'root systems' and 'star complements', and it aims to bring together all the principal results of this area. An important resource for all researchers with an interest in algebraic graph theory.

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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.