On the Hosoya Hyperindex and the Molecular Indices Based on a New Decomposition of the Hosoya Z Matrix

Vicente Garcia Espeso, Jose Javier Molins Vara,
Beatriz Roy Lazaro, Felix Riera Parcerisas, and Dejan Plavsic

Institut Quimic de Sarria, Universitat Ramon Llull, Barcelona, Spain
Enginyeria La Salle, Universitat Ramon Llull, Barcelona, Spain
$The R. Boskovic Institute, Zagreb, Croatia


The decomposition of the Hosoya Z matrix into the sum of kZ matrices,  k = 0, 1, 2, ...,  is proposed. The kZ matrix is based on the independent  sets of  k edges of the spanning subgraphs generated in the construction of  the Z matrix. The Hosoya hyperindex H and a set of structurally related molecular indices kZ defined as the sum of all off-diagonal entries in the  upper triangle of the Z matrix and the corresponding kZ matrices, respectively, are put forward and  studied analytically.