Description:
This book presents results established over the past 40 years on Laplacian matrices of graphs developed using combinatorial matrix theory. The author focuses on the spectrum of Laplacian matrices, the algebraic connectivity of graphs, associated eigenvectors of the Laplacian matrix, and submatrices of the Laplacian matrix. All of these topics illustrate how the properties of a matrix can provide information about the associated graph and vice versa. The text also covers relevant parts of graph theory, Laplacian matrices, and combinatorial matrix theory and includes sources for each theorem.
Review Quotes:
... 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