Spectral Meaning of Coefficients Within the Adjacency Matrix Eigenfunctions of Chemical Graphs of Alkanes

摘要

Adjacency matrix (AM) eigenfunctions of isospectral chemical graphs of alkanes (C_nH_2n+2), in terms of atoms (G~a_Ch) and bonds (G~b_Ch), have been studied. The two eigenfunctions Φ_i and Ψ_i of the AMs A(G~a_Ch) and A(G~b_Ch) referring to the same eigenvalue ε_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 Φ_i and Ψ_i proved to be of common global constitution. Interrela- tions between the local structures of functionsΦ_i and Ψ_i have been also established.