Abstract
The characteristic polynomial of a structure (molecule or a graph) is usually expressed as a function ofx. Here we explore an alternative representation of characteristic polynomials expressed in terms ofL n , the characteristic polynomials of linear chains havingn atoms. While the new forms of the characteristic polynomials are mathematically equivalent to the old forms, they appear to reflect selected structural similarities among homologous molecules better. Besides arriving at general expressions for the form of the characteristic polynomials for numerous families of compounds previously unavailable, the approach is of some interest for the old problem of graph isomorphism and graph recognition in cases of structures which can be associated with a homologous series.
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Operated for the U.S. Department of Energy by Iowa State University under contract no. W-7405-ENG-82. This work was supported in part by the Office of the Director.
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Randić, M. On alternative form of the characteristic polynomial and the problem of graph recognition. Theoret. Chim. Acta 62, 485–498 (1983). https://doi.org/10.1007/BF00557925
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DOI: https://doi.org/10.1007/BF00557925