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

Front Cover
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.
 

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Contents

Introduction
1
Forbidden subgraphs
25
Root systems
64
Regular graphs
88
Star Complements
112
The maximal exCeptional graphs
139
MisCellaneous results
164
Appendix
193
Table A3 Regular exceptional graphs and their spectra
213
Table A4 A construction of the 68 connected regular graphs which
228
Table A5 Onevertex extensions of exceptional star complements
243
Table A6 The maximal exceptional graphs
249
Table A7 The index and vertex degrees of the maximal exceptional
273
Bibliography
281
Index of symbols and terms
295
Copyright

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Page 287 - A geometric characterization of the line graph of a projective plane, J.
Page 285 - Cvetkovic D., Rowlinson P., Simic SK, Graphs with least eigenvalue — 2: the star complement technique, J. Algebraic Combinatorics 1 4(200 1 ), 5-16.

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