Acyclic Molecules Subspectral to Butadiene

The occurence of common eigenvalues, inclusion of spectra of a smaller molecular graph in a larger one, is treated in a systematic way. Emphasis is placed on the detection and construction of concealed acyclic species containing eigenvalues ±1.618 and ±0.618 which can not be recognized by symmetry analysis and Heilbronner procedure. The methodogy is based on the partitioning of secular equation formulated in terms of the contraction and expansion of graphs displayed in Eqs.（3）-（6） and Eqs. （9.1） and （9.2）. Larger subspectral species can be derived from smaller one by expansion without missing the inherent.subspectrality exemplified in Channels 1 and 2. Acyclic molecules subspectral to butadiene are tabulated up to N=15 vertices.