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Quest for molecular graphs with maximal energy: a computer experiment.

I Gutman1, D Vidović

  • 1Faculty of Science, University of Kragujevac, P.O. Box 60, YU-34000 Kragujevac, Yugoslavia. gutman@knez.uis.kg.ac.yu

Journal of Chemical Information and Computer Sciences
|August 14, 2001
PubMed
Summary

Researchers explored molecular graph energy, finding that even-vertex graphs with many six-membered cycles and odd-vertex graphs with six- and five-membered cycles may possess maximal energy.

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Area of Science:

  • Chemical Graph Theory
  • Computational Chemistry
  • Mathematical Chemistry

Background:

  • The energy of a graph G, defined as the sum of the absolute values of its eigenvalues (lambda), is closely related to the pi-electron energy of molecular graphs representing conjugated hydrocarbons.
  • Determining the molecular graph with maximal energy for a given number of vertices (n) and edges (m) remains an open problem, except for specific cases (m=n-1, m=n).

Purpose of the Study:

  • To investigate molecular graphs with maximal energy by constructing and analyzing molecular (n,m)-graphs.
  • To identify structural features that correlate with high graph energy, contributing to solving the maximal energy graph problem.

Main Methods:

  • Employed a Monte Carlo-type construction method to generate molecular graphs with a specified number of vertices (n) and edges (m).

Related Experiment Videos

  • Systematically recorded graphs exhibiting the highest observed energies during the construction process.

    • Main Results:

    • For molecular graphs with an even number of vertices (n), the study suggests that graphs with a high prevalence of six-membered cycles tend to have maximal energy.
    • For molecular graphs with an odd number of vertices (n), the results indicate a preference for structures incorporating both six- and five-membered cycles to achieve maximal energy.

    Conclusions:

    • The findings provide insights into the structural characteristics associated with maximal energy in molecular graphs.
    • This research advances the understanding of graph energy and its relationship to molecular structure, offering potential directions for future studies on extremal graph theory in chemistry.