THE LAPLACIAN MATRIX IN CHEMISTRY

The Laplacian matrix, its spectrum, and its polynomial are discussed. An algorithm for computing the number of spanning trees of a polycycli c graph, based on the corresponding Laplacian spectrum, is outlined. A lso, a technique using the Le Verrier-Faddeev-Frame method for computi ng the Laplacian polynomial of a graph is detailed. In addition, it is shown that the Wiener index of an alkane tree can be given in terms o f its Laplacian spectrum. Two Mohar indices, one based on the Laplacia n spectrum of a molecular graph G and the other based on the Laplacian x2 eigenvalue of G, have been tested in the structure-property relati onships for octanes.