Secular polynomials (SPs) have been constructed and studied for the adjacency matrices A(G;,) and A(G&,) corresponding to chemical graphs of alkanes in terms of atoms (G: , ) and in terms of bonds (G:,). The three second-class Chebyshev polynomials U,(Q), U,-,(Q), and U,-,(Q), with respect to the variable Q proportional to the SP of an isolated CH,-like subgraph, have been shown to appear within both SPs P[ A(G$,)] and P[ A(G&)] and to play the role of algebraic analogues of a (CH,),-like subgraph. Common noncanonical algebraic expressions for both SPs reflecting the regular internal structure of alkanes have been constructed on this basis. Spectral properties of both graphs GEh and GEh have been shown to be determined by those of U,(Q), e g , the band limits of spectra proved to be related to the orthogonality interval Q = [ -1; 11 for polynomials U,(Q). Since the adjacency matrices (AMs) A(($,), but not A(G&), are proportional to definite model Hamiltonian matrices, the obtained results serve to interpret the one-electron spectra of alkanes in terms of peculiarities of usual chemical structure.