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. Technical descriptions of these graphs are included in the appendices, while the bibliography provides over 250 references. It will be an important resource for all researchers with an interest in algebraic graph theory.
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"This work deserves a place on the bookshelf of the mathematician with a serious interest in the theory of graph spectra." - Mathematical Reviews, M. Doob
Book Description
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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Inside This Book
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First Sentence:
In Section 1.1 we introduce notation and terminology which will be used throughout the book. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Interlacing Theorem, Proof Let New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In Section 1.1 we introduce notation and terminology which will be used throughout the book. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Interlacing Theorem, Proof Let New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 19
books:
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- Linear Algebra (Oxford Science Publications) by Richard Kaye in Back Matter (1), and Back Matter (2)
- Linear Algebra by A. Ramachandra Rao in Back Matter (1), and Back Matter (2)
- Algebraic Graph Theory (Cambridge Mathematical Library) by Norman Biggs in Back Matter
- Linear Algebra, 4th Edition by Stephen H. Friedberg in Back Matter
- Problems and Theorems in Linear Algebra (Translations of Mathematical Monographs) by V. V. Prasolov in Back Matter
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