Topics in Algebraic Graph Theory.:
There is no other book with such a wide scope of both areas of algebraic graph theory.
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | , |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge :
Cambridge University Press,
2004.
|
| Series: | Encyclopedia of mathematics and its applications.
|
| Subjects: | |
| Online Access: | DE-862 DE-863 |
| Summary: | There is no other book with such a wide scope of both areas of algebraic graph theory. |
| Item Description: | 1. Introduction. |
| Physical Description: | 1 online resource (294 pages). |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9781107095847 1107095840 9781107089532 1107089530 |
Staff View
MARC
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| 490 | 1 | |a Encyclopedia of Mathematics and its Applications ; |v v. 102 | |
| 505 | 0 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 500 | |a 1. Introduction. | ||
| 520 | |a There is no other book with such a wide scope of both areas of algebraic graph theory. | ||
| 588 | 0 | |a Print version record. | |
| 504 | |a Includes bibliographical references and index. | ||
| 650 | 0 | |a Graph theory. |0 http://id.loc.gov/authorities/subjects/sh85056471 | |
| 650 | 6 | |a Théorie des graphes. | |
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| 700 | 1 | |a Wilson, Robin J. | |
| 700 | 1 | |a Cameron, Peter J. | |
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| author | Beineke, Lowell W. |
| author2 | Wilson, Robin J. Cameron, Peter J. |
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| author_facet | Beineke, Lowell W. Wilson, Robin J. Cameron, Peter J. |
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| 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. |
| ctrlnum | (OCoLC)850148882 |
| dewey-full | 511/.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.5 |
| dewey-search | 511/.5 |
| dewey-sort | 3511 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2025-03-18T14:21:16Z |
| institution | BVB |
| isbn | 9781107095847 1107095840 9781107089532 1107089530 |
| language | English |
| oclc_num | 850148882 |
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| series | Encyclopedia of mathematics and its applications. |
| series2 | Encyclopedia of Mathematics and its Applications ; |
| spelling | Beineke, Lowell W. Topics in Algebraic Graph Theory. Cambridge : Cambridge University Press, 2004. 1 online resource (294 pages). text txt rdacontent computer c rdamedia online resource cr rdacarrier Encyclopedia of Mathematics and its Applications ; v. 102 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. There is no other book with such a wide scope of both areas of algebraic graph theory. Print version record. Includes bibliographical references and index. Graph theory. http://id.loc.gov/authorities/subjects/sh85056471 Théorie des graphes. MATHEMATICS Graphic Methods. bisacsh Graph theory fast Graphentheorie gnd http://d-nb.info/gnd/4113782-6 Wilson, Robin J. Cameron, Peter J. Print version: Beineke, Lowell W. Topics in Algebraic Graph Theory. Cambridge : Cambridge University Press, ©2004 9780521801973 Encyclopedia of mathematics and its applications. http://id.loc.gov/authorities/names/n42010632 |
| spellingShingle | Beineke, Lowell W. Topics in Algebraic Graph Theory. Encyclopedia of mathematics and its applications. 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. Graph theory. http://id.loc.gov/authorities/subjects/sh85056471 Théorie des graphes. MATHEMATICS Graphic Methods. bisacsh Graph theory fast Graphentheorie gnd http://d-nb.info/gnd/4113782-6 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85056471 http://d-nb.info/gnd/4113782-6 |
| title | Topics in Algebraic Graph Theory. |
| title_auth | Topics in Algebraic Graph Theory. |
| title_exact_search | Topics in Algebraic Graph Theory. |
| title_full | Topics in Algebraic Graph Theory. |
| title_fullStr | Topics in Algebraic Graph Theory. |
| title_full_unstemmed | Topics in Algebraic Graph Theory. |
| title_short | Topics in Algebraic Graph Theory. |
| title_sort | topics in algebraic graph theory |
| topic | Graph theory. http://id.loc.gov/authorities/subjects/sh85056471 Théorie des graphes. MATHEMATICS Graphic Methods. bisacsh Graph theory fast Graphentheorie gnd http://d-nb.info/gnd/4113782-6 |
| topic_facet | Graph theory. Théorie des graphes. MATHEMATICS Graphic Methods. Graph theory Graphentheorie |
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