LAPLACIAN MATRICES OF GRAPHS - A SURVEY

Let G be a graph on n vertices. Its Laplacian matrix is the n-by-n matrix L(G) - D(G) - A(G), where A(G) is the familiar (0, 1) adjacency matrix, and D(G) is the diagonal matrix of vertex degrees. This is primarily an expository article surveying some of the many results known for Laplacian matrices. Its six sections are: Introduction, The Spectrum, The Algebraic Connectivity, Congruence and Equivalence, Chemical Applications, and Immanants.