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

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 uni...

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Main Authors:	Raúl M. Falcón, Óscar J. Falcón, Juan Núñez
Format:	Article
Language:	English
Published:	MDPI AG 2019-11-01
Series:	Mathematics
Subjects:	evolution theory evolution algebra mitotic cell cycle total-colored graph
Online Access:	https://www.mdpi.com/2227-7390/7/11/1068

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spelling	doaj-cfe8ed337c164e33a0fbc803ff5b52872020-11-25T02:03:10ZengMDPI AGMathematics2227-73902019-11-01711106810.3390/math7111068math7111068An Application of Total-Colored Graphs to Describe Mutations in Non-Mendelian GeneticsRaúl M. Falcón0Óscar J. Falcón1Juan Núñez2Department of Applied Mathematics I, University of Seville, 41012 Sevilla, SpainDepartment of Geometry and Topology, University of Seville, 41012 Sevilla, SpainDepartment of Geometry and Topology, University of Seville, 41012 Sevilla, SpainAny 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 <i>S</i>-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.https://www.mdpi.com/2227-7390/7/11/1068evolution theoryevolution algebramitotic cell cycletotal-colored graph
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Raúl M. Falcón Óscar J. Falcón Juan Núñez
spellingShingle	Raúl M. Falcón Óscar J. Falcón Juan Núñez An Application of Total-Colored Graphs to Describe Mutations in Non-Mendelian Genetics Mathematics evolution theory evolution algebra mitotic cell cycle total-colored graph
author_facet	Raúl M. Falcón Óscar J. Falcón Juan Núñez
author_sort	Raúl M. Falcón
title	An Application of Total-Colored Graphs to Describe Mutations in Non-Mendelian Genetics
title_short	An Application of Total-Colored Graphs to Describe Mutations in Non-Mendelian Genetics
title_full	An Application of Total-Colored Graphs to Describe Mutations in Non-Mendelian Genetics
title_fullStr	An Application of Total-Colored Graphs to Describe Mutations in Non-Mendelian Genetics
title_full_unstemmed	An Application of Total-Colored Graphs to Describe Mutations in Non-Mendelian Genetics
title_sort	application of total-colored graphs to describe mutations in non-mendelian genetics
publisher	MDPI AG
series	Mathematics
issn	2227-7390
publishDate	2019-11-01
description	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 <i>S</i>-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.
topic	evolution theory evolution algebra mitotic cell cycle total-colored graph
url	https://www.mdpi.com/2227-7390/7/11/1068
work_keys_str_mv	AT raulmfalcon anapplicationoftotalcoloredgraphstodescribemutationsinnonmendeliangenetics AT oscarjfalcon anapplicationoftotalcoloredgraphstodescribemutationsinnonmendeliangenetics AT juannunez anapplicationoftotalcoloredgraphstodescribemutationsinnonmendeliangenetics AT raulmfalcon applicationoftotalcoloredgraphstodescribemutationsinnonmendeliangenetics AT oscarjfalcon applicationoftotalcoloredgraphstodescribemutationsinnonmendeliangenetics AT juannunez applicationoftotalcoloredgraphstodescribemutationsinnonmendeliangenetics
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An Application of Total-Colored Graphs to Describe Mutations in Non-Mendelian Genetics

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