On the surface, matrix theory and graph theory seem like very different branches of mathematics. However, adjacency, Laplacian, and incidence matrices are commonly used to represent graphs, and many properties of matrices can give us useful information about the structure of graphs.Applications of Combinatorial Matrix Theory to Laplacian Matrices o
Rezensionen / Stimmen
... this book works well as a reference textbook for undergraduates. Indeed, it is a distillation of a number of key results involving, specifically, the Laplacian matrix associated with a graph (which is sometimes called the 'nodal admittance matrix' by electrical engineers). ... Molitierno's book represents a well-written source of background on this growing field. The sources are some of the seminal ones in the field, and the book is accessible to undergraduates.
-John T. Saccoman, MAA Reviews, October 2012
The book owes its textbook appeal to detailed proofs, a large number of fully elaborated examples and observations, and a handful of exercises, making beginning graduate students as well as advanced undergraduates its primary audience. Still, it can serve as useful reference book for experienced researchers as well.
-Zentralblatt MATH
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ISBN-13
978-1-040-18747-0 (9781040187470)
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Schweitzer Klassifikation
Matrix Theory Preliminaries. Graph Theory Preliminaries. Introduction to Laplacian Matrices. Algebraic Connectivity. The Fiedler Vector and Bottleneck Matrices for Trees. Bottleneck Matrices for Graphs. The Group Inverse of the Laplacian Matrix.
