| Description |
1 online resource |
| Physical Medium |
polychrome |
| Description |
text file |
| Contents |
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. |
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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. |
| Summary |
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-theoretic approach to the calculation of the number of spanning trees. The authors envision this as a research aid that is of particular interest to graduate students or advanced undergraduate students and researchers in the area of network reliability theory. This would encompass graph theorists of all s. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Trees (Graph theory)
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Trees (Graph theory) |
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Algebra -- Graphic methods.
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Algebra -- Graphic methods. |
| Genre/Form |
Electronic books.
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Electronic books.
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| Added Author |
Saccoman, John T., 1964- author.
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Suffel, Charles L., author.
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| Other Form: |
Print version: Gross, Daniel J. Spanning Tree Results for Graphs and Multigraphs : A Matrix-Theoretic Approach. Singapore : World Scientific Publishing Company, ©2014 9789814566032 |
| ISBN |
9789814566049 (electronic book) |
|
9814566047 (electronic book) |
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9789814566032 |
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