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The permanental polynomial.

G G Cash1

  • 1Risk Assessment Division, U.S. Environmental Protection Agency, Washington, DC 20460, USA. cash.gordon@epa.gov

Journal of Chemical Information and Computer Sciences
|October 25, 2000
PubMed
Summary

This study explores the permanental polynomial of chemical graphs, detailing its properties and applications. A new computer program is introduced for calculating this polynomial from adjacency matrices.

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Area of Science:

  • Chemical Graph Theory
  • Combinatorial Chemistry
  • Computational Chemistry

Background:

  • The permanental polynomial is a valuable invariant in graph theory with applications in chemistry.
  • Understanding its properties is crucial for analyzing molecular structures and their characteristics.

Purpose of the Study:

  • To identify and discuss the properties and uses of the permanental polynomial for unweighted chemical graphs.
  • To provide coefficients and zeroes for representative chemical structures.
  • To describe a computational tool for calculating the permanental polynomial.

Main Methods:

  • Analysis of adjacency matrices of unweighted chemical graphs.
  • Calculation and examination of the permanental polynomial's coefficients and zeroes.
  • Development of a computer program for polynomial computation.

Main Results:

  • Identification of key properties and applications of the permanental polynomial in chemical graph theory.
  • Presentation of specific polynomial coefficients and zeroes for various chemical structures.
  • Successful development of a computer program for calculating the permanental polynomial.

Conclusions:

  • The permanental polynomial offers significant insights into the properties of chemical graphs.
  • The developed computational tool facilitates further research in this area.
  • This work contributes to the application of graph theory in chemistry.

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