On the Hosoya hyperindex and the molecular indices based on a new decomposition of the Hosoya Z matrix

The decomposition of the Hosoya Z matrix into the sum of (k)Z matrices, k = 0, 1, 2, ..., is proposed. The (k)Z 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 (k)Z defined as the sum of all off-diagonal entries in the upper triangle of the Z matrix and the corresponding (k)Z matrices, respectively, are put forward and studied analytically.