The Resource Topics in algebraic graph theory, edited by Lowell W. Beineke, Robin J. Wilson ; academic consultant, Peter J. Cameron, (electronic resource)

Topics in algebraic graph theory, edited by Lowell W. Beineke, Robin J. Wilson ; academic consultant, Peter J. Cameron, (electronic resource)

Label
Topics in algebraic graph theory
Title
Topics in algebraic graph theory
Statement of responsibility
edited by Lowell W. Beineke, Robin J. Wilson ; academic consultant, Peter J. Cameron
Contributor
Subject
Genre
Language
  • eng
  • eng
Summary
There is no other book with such a wide scope of both areas of algebraic graph theory
Member of
Cataloging source
MiAaPQ
Dewey number
511/.5
Illustrations
illustrations
Index
index present
Language note
English
LC call number
QA166
LC item number
.T64 2005
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
  • Beineke, Lowell W
  • Wilson, Robin J
  • Cameron, Peter J
Series statement
  • Encyclopedia of mathematics and its applications
  • Encyclopedia of Mathematics and its Applications
Series volume
v. 102
http://library.link/vocab/subjectName
Graph theory
Label
Topics in algebraic graph theory, edited by Lowell W. Beineke, Robin J. Wilson ; academic consultant, Peter J. Cameron, (electronic resource)
Instantiates
Publication
Note
Reprinted 2007
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • Cover; Topics in Algebraic Graph Theory; Series Page; Title; Copyright; Contents; Preface; Foreword; Introduction; 1. Graph theory; Graphs; Variations of graphs; Adjacency and degrees; Walks; Distance; Subgraphs; Connectedness and connectivity; Bipartite graphs; Trees; Special graphs; Operations on graphs; Traversability; Planarity; Graph colourings; Line graphs; Directed graphs; 2. Linear algebra; The space Rn; Metric properties; Vector spaces; Subspaces; Bases; Dimension; Euclidean spaces; Linear transformations; Algebra of linear transformations; The matrix of a linear transformation
  • Operations on matricesTypes of matrices; Determinants; Change of basis; Eigenvalues and eigenvectors; Diagonalizing matrices; Quadratic forms; 3. Group theory; Groups; Homomorphisms; Subgroups; Composition series; Finite simple groups; Permutation groups; Products; Automorphism groups of graphs; Orbits and stabilizers; Group actions; Transitivity; Orbitals and rank; Graphs admitting a given group; Primitivity and double transitivity; References; 1 Eigenvalues of graphs; 1. Introduction; 2. Some examples; 3. A little matrix theory; 4. Eigenvalues and walks; Strongly regular graphs
  • Distance-regular graphs5. Eigenvalues and labellings of graphs; 6. Lower bounds for the eigenvalues; 7. Upper bounds for the eigenvalues; 8. Other matrices related to graphs; 9. Cospectral graphs; Using graph operations; Pasting graphs together; References; 2 Graphs and matrices; 1. Introduction; 2. Some classical theorems; 3. Digraphs; 4. Biclique partitions of graphs; 5. Bipartite graphs; 6. Permanents; 7. Converting the permanent into the determinant; 8. Chordal graphs and perfect Gaussian elimin; 9. Ranking players in tournaments; References; 3 Spectral graph theory; 1. Introduction
  • 2. Angles3. Star sets and star partitions; 4. Star complements; 5. Exceptional graphs; 6. Reconstructing the characteristic polynomial; 7. Non-complete extended p-sums of graphs; 8. Integral graphs; References; 4 Graph Laplacians; 1. Introduction; 2. The Laplacian of a graph; 3. Laplace eigenvalues; Bounding the Laplace eigenvalues; Eigenvalues of the transition Laplacian; 4. Eigenvalues and vertex partitions of graphs; The bipartition width; 5. The max-cut problem and semi-definite programming; 6. Isoperimetric inequalities; 7. The travelling salesman problem; 8. Random walks on graphs
  • Rate of convergence of a random walkReferences; 5 Automorphisms of graphs; 1. Graph automorphisms; 2. Algorithmic aspects; 3. Automorphisms of typical graphs; 4. Permutation groups; 5. Abstract groups; 6. Cayley graphs; 7. Vertex-transitive graphs; 8. Higher symmetry; 9. Infinite graphs; 10. Graph homomorphisms; References; 6 Cayley graphs; 1. Introduction; 2. Recognition; 3. Special examples; 4. Prevalence; 5. Isomorphism; 6. Enumeration; 7. Automorphisms; 8. Subgraphs; 9. Hamiltonicity; 10. Factorization; 11. Embeddings; 12. Applications; References; 7 Finite symmetric graphs
  • 1. Introduction
Dimensions
unknown
Extent
1 online resource (294 p.)
Form of item
online
Isbn
9781107103924
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)2550000001095233
  • (EBL)1178975
  • (OCoLC)850148882
  • (SSID)ssj0000916460
  • (PQKBManifestationID)12431781
  • (PQKBTitleCode)TC0000916460
  • (PQKBWorkID)10877750
  • (PQKB)10716252
  • (MiAaPQ)EBC1178975
  • (EXLCZ)992550000001095233
Label
Topics in algebraic graph theory, edited by Lowell W. Beineke, Robin J. Wilson ; academic consultant, Peter J. Cameron, (electronic resource)
Publication
Note
Reprinted 2007
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • Cover; Topics in Algebraic Graph Theory; Series Page; Title; Copyright; Contents; Preface; Foreword; Introduction; 1. Graph theory; Graphs; Variations of graphs; Adjacency and degrees; Walks; Distance; Subgraphs; Connectedness and connectivity; Bipartite graphs; Trees; Special graphs; Operations on graphs; Traversability; Planarity; Graph colourings; Line graphs; Directed graphs; 2. Linear algebra; The space Rn; Metric properties; Vector spaces; Subspaces; Bases; Dimension; Euclidean spaces; Linear transformations; Algebra of linear transformations; The matrix of a linear transformation
  • Operations on matricesTypes of matrices; Determinants; Change of basis; Eigenvalues and eigenvectors; Diagonalizing matrices; Quadratic forms; 3. Group theory; Groups; Homomorphisms; Subgroups; Composition series; Finite simple groups; Permutation groups; Products; Automorphism groups of graphs; Orbits and stabilizers; Group actions; Transitivity; Orbitals and rank; Graphs admitting a given group; Primitivity and double transitivity; References; 1 Eigenvalues of graphs; 1. Introduction; 2. Some examples; 3. A little matrix theory; 4. Eigenvalues and walks; Strongly regular graphs
  • Distance-regular graphs5. Eigenvalues and labellings of graphs; 6. Lower bounds for the eigenvalues; 7. Upper bounds for the eigenvalues; 8. Other matrices related to graphs; 9. Cospectral graphs; Using graph operations; Pasting graphs together; References; 2 Graphs and matrices; 1. Introduction; 2. Some classical theorems; 3. Digraphs; 4. Biclique partitions of graphs; 5. Bipartite graphs; 6. Permanents; 7. Converting the permanent into the determinant; 8. Chordal graphs and perfect Gaussian elimin; 9. Ranking players in tournaments; References; 3 Spectral graph theory; 1. Introduction
  • 2. Angles3. Star sets and star partitions; 4. Star complements; 5. Exceptional graphs; 6. Reconstructing the characteristic polynomial; 7. Non-complete extended p-sums of graphs; 8. Integral graphs; References; 4 Graph Laplacians; 1. Introduction; 2. The Laplacian of a graph; 3. Laplace eigenvalues; Bounding the Laplace eigenvalues; Eigenvalues of the transition Laplacian; 4. Eigenvalues and vertex partitions of graphs; The bipartition width; 5. The max-cut problem and semi-definite programming; 6. Isoperimetric inequalities; 7. The travelling salesman problem; 8. Random walks on graphs
  • Rate of convergence of a random walkReferences; 5 Automorphisms of graphs; 1. Graph automorphisms; 2. Algorithmic aspects; 3. Automorphisms of typical graphs; 4. Permutation groups; 5. Abstract groups; 6. Cayley graphs; 7. Vertex-transitive graphs; 8. Higher symmetry; 9. Infinite graphs; 10. Graph homomorphisms; References; 6 Cayley graphs; 1. Introduction; 2. Recognition; 3. Special examples; 4. Prevalence; 5. Isomorphism; 6. Enumeration; 7. Automorphisms; 8. Subgraphs; 9. Hamiltonicity; 10. Factorization; 11. Embeddings; 12. Applications; References; 7 Finite symmetric graphs
  • 1. Introduction
Dimensions
unknown
Extent
1 online resource (294 p.)
Form of item
online
Isbn
9781107103924
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)2550000001095233
  • (EBL)1178975
  • (OCoLC)850148882
  • (SSID)ssj0000916460
  • (PQKBManifestationID)12431781
  • (PQKBTitleCode)TC0000916460
  • (PQKBWorkID)10877750
  • (PQKB)10716252
  • (MiAaPQ)EBC1178975
  • (EXLCZ)992550000001095233

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