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Computer program for finding all possible cycles in graphs.

Alexandru T Balaban1, Petru Filip2, Teodor-Silviu Balaban2

  • 1The Polytechnic Institute, Organic Chemistry Department, Splaiul Independenţei 313, 76206 Bucharest, Roumania.

Journal of Computational Chemistry
|November 23, 2017
PubMed
Summary
This summary is machine-generated.

This study introduces a novel algorithm for identifying all cycles in graphs by analyzing edge combinations in a reduced graph structure. The method efficiently lists cycles by increasing size, providing a unique numbering for each.

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Area of Science:

  • Graph Theory
  • Computational Mathematics
  • Computer Science

Background:

  • Identifying cycles in graphs is a fundamental problem with applications in various scientific and engineering fields.
  • Existing methods may face challenges with scalability or efficiency when dealing with large or complex graphs.

Purpose of the Study:

  • To present a new, efficient algorithm for the exhaustive identification of all possible cycles within a given graph.
  • To develop a systematic approach for enumerating cycles based on graph structure and edge connectivity.

Main Methods:

  • Construction of a homeomorphically reduced graph (HRG) by excluding vertices with degrees less than three.
  • Iterative generation and testing of edge combinations within the HRG to detect cycle-forming structures.
  • A novel cycle numbering system and arrangement of results by increasing ring size.

Main Results:

  • The algorithm successfully identifies all unique cycles in a graph.
  • Cycles are systematically listed in order of increasing size, facilitating analysis.
  • A computer program implementing the algorithm is provided, with performance metrics (computing times) detailed.

Conclusions:

  • The presented approach offers an effective method for complete graph cycle identification.
  • The HRG-based strategy and systematic enumeration provide a robust solution for cycle detection problems.
  • The developed algorithm and program are valuable tools for researchers in graph theory and related computational fields.