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Spanning tree results for graphs and multigraphs : a matrix-theoretic approach /
This book is concerned with the optimization problem of maximizing the number of spanning trees of a multigraph. Since a spanning tree is a minimally connected subgraph, graphs and multigraphs having more of these are, in some sense, immune to disconnection by edge failure. We employ a matrix-theore...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New Jersey :
World Scientific,
[2014]
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Preface; Contents; 0 An Introduction to Relevant Graph Theory and Matrix Theory; 0.1 Graph Theory; 0.2 Matrix Theory; 1 Calculating the Number of Spanning Trees: The Algebraic Approach; 1.1 The Node-Arc Incidence Matrix; 1.2 Laplacian Matrix; 1.3 Special Graphs; 1.4 Temperley's B-Matrix; 1.5 Multigraphs; 1.6 Eigenvalue Bounds for Multigraphs; 1.7 Multigraph Complements; 1.8 Two Maximum Tree Results; 2 Multigraphs with the Maximum Number of Spanning Trees: An Analytic Approach; 2.1 The Maximum Spanning Tree Problem; 2.2 Two Maximum Spanning Tree Results; 3 Threshold Graphs.
- 3.1 Characteristic Polynomials of Threshold Graphs3.2 Minimum Number of Spanning Trees; 3.3 Spanning Trees of Split Graphs; 4 Approaches to the Multigraph Problem; 5 Laplacian Integral Graphs and Multigraphs; 5.1 Complete Graphs and Related Structures; 5.2 Split Graphs and Related Structures; 5.3 Laplacian Integral Multigraphs; Bibliography; Index.