An Illustration of Chemical Mathematics Subspectral Graphs

FIGURE 4.5 The molecular graph of hexatriene with coefficients for the symmetric and antisymmetric eigenvectors inscribed on pyrene and biphenylene graphs illustrating the same sum rule for their coefficients. 

FIGURE 4.6 The coefficients of the leading eigenvector of hexatriene (a, b, c) and the coefficients of tetracene derivative, which satisfy the same sum rules. 

Find additional molecular structures containing the eigenvalues of hexatriene 1.8019, 1.2470, 0.4450, but having no nodes on atoms. 

Select an arbitrary smaller graph. Find additional graphs thatsatisfy the same sum mies for their coefficients, which will then contain the eigenvalues of the smaller graph. 

For additional illustrations of subspectral conjugated molecular systems, see a paper by Dias [40] on a series of molecular graphs having a preponderance of common eigenvalues in which, for a collection of subspectral structures, their eigenvalues are tabulated. 

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