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An Application of Total-Colored Graphs to Describe Mutations in Non-Mendelian Genetics

Author

Listed:
  • Raúl M. Falcón

    (Department of Applied Mathematics I, University of Seville, 41012 Sevilla, Spain)

  • Óscar J. Falcón

    (Department of Geometry and Topology, University of Seville, 41012 Sevilla, Spain)

  • Juan Núñez

    (Department of Geometry and Topology, University of Seville, 41012 Sevilla, Spain)

Abstract

Any gene mutation during the mitotic cell cycle of a eukaryotic cell can be algebraically represented by an isotopism of the evolution algebra describing the genetic pattern of the inheritance process. We identify any such pattern with a total-colored graph so that any isotopism of the former is uniquely related to an isomorphism of the latter. This enables us to develop some results on graph theory in the context of the molecular processes that occur during the S -phase of a mitotic cell cycle. In particular, each monochromatic subset of edges is identified with a mutation or regulatory mechanism that relates any two statuses of the genotypes of a pair of chromatids.

Suggested Citation

  • Raúl M. Falcón & Óscar J. Falcón & Juan Núñez, 2019. "An Application of Total-Colored Graphs to Describe Mutations in Non-Mendelian Genetics," Mathematics, MDPI, vol. 7(11), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1068-:d:284314
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