Isospectral graphs and molecules

Herndon, William C.; Ellzey, M. L.

doi:10.1016/0040-4020(75)85002-2

Cited by 83 publications

(27 citation statements)

References 21 publications

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“…The concept of cospectral vertices was introduced in [9]. A characterization of cospectral vertices by their eigenvectors is found in [7] and also reported in [lo]. Herndon and Ellzey [7] also introduced the concept of unrestricted substitution vertices and used this to extend the utility of cospectral vertices sufficiently to construct eighteen of the thirty-three connected cospectral pairs on seven vertices.…”

Section: Related Resultsmentioning

confidence: 99%

The Construction of Cospectral Composite Graphs

Schwenk

Ellzey

1979

Annals of the New York Academy of Sciences

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Summary An operation loosely described as a type of composition of graphs is studied. Under rather flexible conditions, the resulting composite graphs must be cospectral. This operation is sufficiently powerful to generate eighty‐one cospectral pairs with at most nine vertices. These pairs include the unique smallest cospectral pair, the smallest cospectral connected pair, and one pair of trees with nine vertices. It is felt that this operation provides a unified explanation of cospectrality in several cases that were previously viewed as coincidental.

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Section: Related Resultsmentioning

confidence: 99%

The Construction of Cospectral Composite Graphs

Schwenk

Ellzey

1979

Annals of the New York Academy of Sciences

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“…Although detailed analysis has not yet been completed, the interesting feature of the genealogies observed here may be due to the appearance of two pairs of endospectral vertices [17,33,34] in a tree graph.…”

Section: Resultsmentioning

confidence: 99%

Chemistry-Relevant Isospectral Graphs. Acyclic Conjugated Polyenes

Hosoya¹

2016

Croat. Chem. Acta

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“…Graph pairs that are cospectrally rooted are characterized by Herndon and Ellzey in [120]. We now turn to the construction techniques of cospectral graphs.…”

Section: Cospectral Graphsmentioning

confidence: 99%