TY  - BOOK
AU  - Gross,Daniel J.
AU  - Saccoman,John T.
AU  - Suffel,Charles L.
TI  - Spanning tree results for graphs and multigraphs: a matrix-theoretic approach 
SN  - 9789814566049
AV  - QA166.2 
U1  - 511.5 23
PY  - 2014///]
CY  - New Jersey
PB  - World Scientific
KW  - Trees (Graph theory)
KW  - Algebra
KW  - Graphic methods
KW  - MATHEMATICS
KW  - General
KW  - bisacsh
KW  - fast
KW  - Electronic books
N1  - 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
N2  - 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
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ER  -