Pregledni rad

Isospectral and Subspectral Molecules

S. S. D'Amato ; Department of Chemistry, University of South Carolina, Columbia, South Carolina 29208, U.S.A.
B. M. Gimarc ; Department of Chemistry, University of South Carolina, Columbia, South Carolina 29208, U.S.A.
N. Trinajstić ; Department of Chemistry, University of South Carolina, Columbia, South Carolina 29208, U.S.A.

Sažetak

Isospectral molecules are non-identical structures which possess
the same spectrum of eigenvalues. Methods for recognizing
isospectrality, procedures of Heilbronner, Herndon and .Zivkovic for
constructing new isospectral mates, and the specification of the
relationship among the eigenvectors of the adjacency matrix of
isospectral pairs are discussed here.
Instances of isospectral graphs are relatively rare. There are
many cases, however, in which the spectrum of one molecular graph
contains the spectrum of a second, smaller graph. In such cases, the
larger, composite, graph and the smaller, component graph are said
to be subspectral. Methods of McClelland, Hall and D'Amato for
determining subspectrality of graphs are reviewed in detail. It
appears that all known cases of subspectral molecules, but one, can
be explained by various decomposition or factorization schemes.
No chemical evidence is found so far that shows a relationship
among the measured properties of isospectral or subspectral molecules.
However, the existence of isospectral and subspectral molecules
prevented the use of characteristic polynomial for the unique
characterization of molecules in various classification schemes and
in computerized chemical documentation.

Ključne riječi

Hrčak ID:

194407

URI

https://hrcak.srce.hr/194407

Datum izdavanja:

15.3.1981.

Posjeta: 737 *