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 AMs 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 coefficients, each associated with a definite carbon atom. As a result, functions Phi(i) and Psi(i) proved to be of common global constitution. Interrelations between the local structures of functions Phi(i) and Psi(i) have been also established. These results have been used to substantiate a hypothesis concerning the spectral meaning of coefficients within eigenfuctions Phi(i) of matrices A(G(Ch)(a)). These coefficients are assumed to determine the extents of participation of individual atoms in the ionization of a molecule from the energy level epsilon(i), although no direct link seems to be present between the AMs A(G(Ch)(a)) and the respective hamiltonian matrices.