Graph theory is an important branch of contemporary combinatorial mathematics. By describing recent results in algebraic graph theory and demonstrating how linear algebra can be used to tackle graph-theoretical problems, the authors provide new techniques for specialists in graph theory. The book explains how the spectral theory of finite graphs can be strengthened by exploiting properties of the eigenspaces of adjacency matrices associated with a graph. The extension of spectral techniques proceeds at three levels: using eigenvectors associated with an arbitrary labeling of graph vertices, using geometrical invariants of eigenspaces such as graph angles and main angles, and introducing certain kinds of canonical eigenvectors by means of star partitions and star bases. Current research on these topics is part of a wider effort to forge closer links between algebra and combinatorics. Problems of graph reconstruction and identification are used to illustrate the importance of graph angles and star partitions in relation to graph structure. Specialists in graph theory will welcome this treatment of important new research.
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"The overall level of writing is advanced, and the book is most suitable for research specialists in graph theory." Telegraphic Reviews
Book Description
This book describes how the spectral theory of finite graphs can be strengthened by exploiting properties of the eigenspaces of adjacency matrices associated with a graph. Current research on this topic may be seen as part of a wider effort to forge closer links between algebra and combinatorics (in particular between linear algebra and graph theory). Specialists in graph theory will welcome this treatment of important new research.
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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 - Statistically Improbable Phrases (SIPs): (learn more)
star partition, canonical star basis, cospectral graphs, cospectral vertices, cospectral regular graphs, same main angles, stepwise adjacency matrix, perturbed graph, unicyclic graphs, main eigenvalue, cospectral pairs, canonical vertex, isospectral graphs, stepwise matrix, generalized direct product, minimal forbidden subgraphs, pendant edge, graph angles, graph isomorphism problem, strongly regular graph, reconstruction conjecture, star cell, angle matrix, graph perturbations, graph spectra Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proposition Let, Proof Suppose, Example Let, Reconstruction Lemma, Definition Let, Reconstruction Theorem, Remark Let, Corollary Let, Lloyd's Theorem, Proof By Lemma New!
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Front Cover | Table of Contents | First Pages | Index | Surprise Me!
In Section 1.1 we introduce notation and terminology which will be used throughout the book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
star partition, canonical star basis, cospectral graphs, cospectral vertices, cospectral regular graphs, same main angles, stepwise adjacency matrix, perturbed graph, unicyclic graphs, main eigenvalue, cospectral pairs, canonical vertex, isospectral graphs, stepwise matrix, generalized direct product, minimal forbidden subgraphs, pendant edge, graph angles, graph isomorphism problem, strongly regular graph, reconstruction conjecture, star cell, angle matrix, graph perturbations, graph spectra Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proposition Let, Proof Suppose, Example Let, Reconstruction Lemma, Definition Let, Reconstruction Theorem, Remark Let, Corollary Let, Lloyd's Theorem, Proof By Lemma New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
Citations (learn more)
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25
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- Graph Theory (Graduate Texts in Mathematics) by Reinhard Diestel on 5 pages
- Recent Results in the Theory of Graph Spectra (Annals of Discrete Mathematics) by Dragos M. Cvetkovic in Front Matter, and Back Matter
- Graph Theory (Wiley Series in Discrete Mathematics and Optimization) by Russell Merris in Back Matter (1), and Back Matter (2)
- Multilinear Algebra (Algebra, Logic and Applications) by Russell Merris in Back Matter (1), and Back Matter (2)
- Linear Algebra (2nd Edition) by Kenneth M Hoffman in Back Matter (1), and Back Matter (2)
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- Topics in Algebraic Graph Theory (Encyclopedia of Mathematics and its Applications) (v. 1) by Lowell W. Beineke in Front Matter, page 111, and Back Matter
- Design Theory: Volume 2 (Encyclopedia of Mathematics and its Applications) by Thomas Beth in Front Matter
- The Mountain Pass Theorem: Variants, Generalizations and Some Applications (Encyclopedia of Mathematics and its Applications) by Youssef Jabri in Front Matter
- Categorical Foundations: Special Topics in Order, Topology, Algebra, and Sheaf Theory (Encyclopedia of Mathematics and its Applications) by Maria Cristina Pedicchio in Front Matter
- Complexity: Introduction and Fundamentals (Mathematical Chemistry, 7) by D.G. Bonchev on page 88
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