Regular Graphs

Name: Regular Graphs | A Spectral Approach
Brand: De Gruyter
Price: 129.95 EUR
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A Spectral Approach

Zoran Stanic(Autor*in)

De Gruyter (Verlag)

1. Auflage

Erschienen am 24. April 2017

XI, 236 Seiten

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978-3-11-035134-7 (ISBN)

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Inhalt

Intro
Preface
Contents
List of Figures
1 Introduction
1.1 Terminology and notation
1.2 Notes on regular graphs
1.3 Elements of the theory of graph spectra
2 Spectral properties
2.1 Basic properties of the spectrum of a regular graph
2.2 Operations on regular graphs and resulting spectra
2.3 Other kinds of graph spectrum
2.3.1 Laplacian and signless Laplacian spectrum
2.3.2 Seidel spectrum
2.4 Deducing regularity from the spectrum
2.5 Spectral distances of regular graphs
2.6 Inequalities for eigenvalues
2.6.1 Second largest eigenvalue
2.6.2 Toughness of regular graphs
2.6.3 More inequalities
2.7 Extremal regular graphs
2.8 Eigenvalue estimation
2.9 Eigenvalue distribution
3 Particular types of regular graph
3.1 Non-complete extended p-sums
3.2 Walk-regular graphs
3.3 Distance-regular graphs
3.3.1 Basic properties
3.3.2 Classical examples
3.3.3 Inequalities for eigenvalues
3.3.4 Geometric graphs
3.3.5 Deducing distance-regularity from the spectrum
3.4 Strongly regular graphs
3.4.1 Basic properties
3.4.2 Small examples
3.4.3 Conference graphs
3.4.4 Generalized Latin squares and partial geometries
3.4.5 Spectral distances
3.5 Kneser graphs
3.6 Regular graphs of line systems
3.6.1 Equidistant lines
3.6.2 Root systems
3.7 Star complements
3.7.1 Reconstruction theorem and its consequences
3.7.2 Star complement technique
3.7.3 Star complements in regular graphs
3.8 Partially balanced incomplete block designs
3.8.1 Balanced incomplete block designs
3.8.2 Partially balanced incomplete block designs with 2 associate classes
4 Determinations of regular graphs
4.1 Exceptional regular graphs
4.1.1 Regular graphs with ?2=1
4.2 Reflexive bipartite regular graphs
4.3 Integral regular graphs
4.3.1 Integral cubic graphs
4.3.2 Integral 4-regular graphs
4.3.3 Integral regular line graphs
4.4 Regular graphs with a small number of distinct eigenvalues
4.4.1 Strongly regular graphs of larger order
4.4.2 Regular graphs with 4 distinct eigenvalues
4.4.3 Bipartite regular graphs with 3 distinct non-negative eigenvalues
4.5 Regular graphs determined by their spectra
4.5.1 Line graphs
4.5.2 Graphs with at most 4 distinct eigenvalues
4.5.3 Some constructions
5 Expanders
5.1 Combinatorial approach
5.2 Algebraic approach
5.3 Random walks
5.4 Constructions
5.4.1 Covers of graphs
5.4.2 Zig-zag product
5.4.3 Examples of Cayley expanders
5.5 Codes from graphs
5.5.1 A probabilistic algorithm
5.5.2 Error correcting codes
6 Distance matrix of regular graphs
6.1 Definition and a Hoffman-like polynomial
6.2 D-spectrum of certain regular graphs
6.3 D-spectrum of distance-regular graphs
6.4 Regular graphs constrained by D-spectrum
References
Graph index
Index

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