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

Raúl M. Falcón, Óscar J. Falcón and Juan Núñez
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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

Mathematics, 2019, vol. 7, issue 11, 1-11

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.

Keywords: evolution theory; evolution algebra; mitotic cell cycle; total-colored graph (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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