Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs

by Jason J. Molitierno

This book presents results established over the past 30 years on the Laplacian matrix 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 give 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.

350 pages, Hardcover

First published January 25, 2012