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Topics in Algebraic Graph Theory.
There is no other book with such a wide scope of both areas of algebraic graph theory.
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2004.
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| Colección: | Encyclopedia of mathematics and its applications.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.