Topics in graph automorphisms and reconstruction /

This in-depth coverage of important areas of graph theory maintains a focus on symmetry properties of graphs. Standard topics on graph automorphisms are presented early on, while in later chapters more specialised topics are tackled, such as graphical regular representations and pseudosimilarity. Th...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Lauri, Josef, 1955- (Autor), Scapellato, Raffaele, 1955- (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge, United Kingdom : Cambridge University Press, 2016.
Edición:Second edition.
Colección:London Mathematical Society lecture note series ; 432.
Temas:
Graph theory.
Automorphisms.
Reconstruction (Graph theory)
Automorphismes.
Reconstruction (Théorie des graphes)
MATHEMATICS > General.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Machine generated contents note: 1. Graphs and Groups: Preliminaries
  • 1.1. Graphs and digraphs
  • 1.2. Groups
  • 1.3. Graphs and groups
  • 1.4. Edge-automorphisms and line-graphs
  • 1.5. word on issues of computational complexity
  • 1.6. Exercises
  • 1.7. Notes and guide to references
  • 2. Various Types of Graph Symmetry
  • 2.1. Transitivity
  • 2.2. Asymmetric graphs
  • 2.3. Graph symmetries and the spectrum
  • 2.4. Simple eigenvalues
  • 2.5. Higher symmetry conditions
  • 2.6. Exercises
  • 2.7. Notes and guide to references
  • 3. Cayley Graphs
  • 3.1. Cayley colour graphs
  • 3.2. Frucht's and Bouwer's Theorems
  • 3.3. Cayley graphs and digraphs
  • 3.4. Doyle-Holt Graph
  • 3.5. Non-Cayley vertex-transitive graphs
  • 3.6. Coset graphs and Sabidussi's Theorem
  • 3.7. Double coset graphs and semisymmetric graphs
  • 3.8. Hamiltonicity
  • 3.9. Characters of abelian groups and Cayley graphs
  • 3.10. Growth rates
  • 3.11. Exercises
  • 3.12. Notes and guide to references
  • 4. Orbital Graphs and Strongly Regular Graphs
  • 4.1. Definitions and basic properties
  • 4.2. Rank 3 groups
  • 4.3. Strongly regular graphs
  • 4.4. Integrality Condition
  • 4.5. Moore graphs
  • 4.6. Exercises
  • 4.7. Notes and guide to references
  • 5. Graphical Regular Representations and Pseudosimilarity
  • 5.1. Elementary results
  • 5.2. Abelian groups
  • 5.3. Pseudosimilarity
  • 5.4. Some basic results
  • 5.5. Several pairs of pseudosimilar vertices
  • 5.6. Several pairs of pseudosimilar edges
  • 5.7. Large sets of mutually pseudosimilar vertices
  • 5.8. Exercises
  • 5.9. Notes and guide to references
  • 6. Products of Graphs
  • 6.1. General products of graphs
  • 6.2. Direct product
  • 6.3. Cartesian product
  • 6.4. More products
  • 6.5. Stability and two-fold automorphisms
  • 6.6. Additional remarks on graph products
  • 6.7. Exercises
  • 6.8. Notes and guide to references
  • 7. Special Classes of Vertex-Transitive Graphs and Digraphs
  • 7.1. Generalised Petersen graphs
  • 7.2. Kneser graphs and odd graphs
  • 7.3. Metacirculant graphs
  • 7.4. quasi-Cayley graphs and digraphs
  • 7.5. Generalised Cayley graphs
  • 7.6. Exercises
  • 7.7. Notes and guide to references
  • 8. Reconstruction Conjectures
  • 8.1. Definitions
  • 8.2. Some basic results
  • 8.3. Maximal planar graphs
  • 8.4. Digraphs and degree-associated reconstruction
  • 8.5. Exercises
  • 8.6. Notes and guide to references
  • 9. Reconstructing from Subdecks
  • 9.1. endvertex-deck
  • 9.2. Reconstruction numbers
  • 9.3. characteristic polynomial deck
  • 9.4. Exercises
  • 9.5. Notes and guide to references
  • 10. Counting Arguments in Vertex-Reconstruction
  • 10.1. Kocay's Lemma
  • 10.2. Counting spanning subgraphs
  • 10.3. characteristic and the chromatic polynomials
  • 10.4. Exercises
  • 10.5. Notes and guide to references
  • 11. Counting Arguments in Edge-Reconstruction
  • 11.1. Definitions and notation
  • 11.2. Homomorphisms of structures
  • 11.3. Lovasz' and Nash-Williams' Theorems
  • 11.4. Extensions
  • 11.5. Exercises
  • 11.6. Notes and guide to references.

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