engleski

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 polycyclic graph, based on the corresponding Laplacian spectrum, is outlined. Also, a technique using the Le Verrier-Faddeev-Frame method for computing 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 of its Laplacian spectrum. Two Mohar indices, one based on the Laplacian spectrum of a molecular graph G and the other based on the Laplacian x2 eigenvalue of G, have been tested in the structure- property relationships for octanes.

characteristic-polynomials ; chemical graphs ; molecular descriptors

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