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On the Graph Isomorphism Completeness of Directed and Multidirected Graphs

Author

Listed:
  • Sebastian Pardo-Guerra

    (Center for Engineered Natural Intelligence, La Jolla, CA 92093, USA
    These authors contributed equally to this work.)

  • Vivek Kurien George

    (Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
    These authors contributed equally to this work.)

  • Gabriel A. Silva

    (Center for Engineered Natural Intelligence, La Jolla, CA 92093, USA
    Department of Bioengineering, University of California, San Diego, CA 92093, USA
    Department of Neurosciences, University of California, San Diego, CA 92093, USA)

Abstract

The category of directed graphs is isomorphic to a particular category whose objects are labeled undirected bipartite graphs and whose morphisms are undirected graph morphisms that respect the labeling. Based on this isomorphism, we begin by showing that the class of all directed graphs is a Graph Isomorphism Complete class. Afterwards, by extending this categorical framework to weighted prime graphs, we prove that the categories of multidirected graphs with and without self-loops are each isomorphic to a particular category of weighted prime graphs. Consequently, we prove that these classes of multidirected graphs are also Graph Isomorphism Complete.

Suggested Citation

  • Sebastian Pardo-Guerra & Vivek Kurien George & Gabriel A. Silva, 2025. "On the Graph Isomorphism Completeness of Directed and Multidirected Graphs," Mathematics, MDPI, vol. 13(2), pages 1-16, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:2:p:228-:d:1564742
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