SPECTRAL MEANING OF COEFFICIENTS WITHIN THE ADJACENCY MATRIX EIGENFUNCTIONS OF CHEMICAL GRAPHS OF ALKANES

Adjacency matrix (AM) eigenfunctions of isospectral chemical graphs of alkanes (CnH2n+2), in terms of atoms (G(Ch)(a)) and bonds (G(Ch)(b)), have been studied. The two eigenfunctions Phi(i) and Psi(i) of the AM s A(G(Ch)(a)) and A(G(Ch)(b)) referring to the same eigenvalue epsilon (i) have been expressed in terms of a common set of n principal coeffi cients, each associated with a definite carbon atom. As a result, func tions Phi(i) and Psi(i) proved to be of common global constitution. In terrelations between the local structures of functions Phi(i) and Psi( i) have been also established. These results have been used to substan tiate a hypothesis concerning the spectral meaning of coefficients wit hin eigenfuctions Phi(i) of matrices A(G(Ch)(a)). These coefficients a re assumed to determine the extents of participation of individual ato ms in the ionization of a molecule from the energy level epsilon(i), a lthough no direct link seems to be present between the AMs A(G(Ch)(a)) and the respective hamiltonian matrices.