Backwards genetic inheritance through coalgebra-graphs

Abstract

We attach two weighted digraphs to any coalgebra C with genetic realization. Algebraically, these digraphs describe the right and left coideal structure of C, whereas genetically they represent the backwards inheritance through the male and female heritage lines, respectively. After establishing the relationship between the strongly connectedness of the attached digraphs and the simplicity of the genetic coalgebras, both digraphs are unified by considering the notion of genetic trigraph.

Keywords:

• Genetic coalgebra
• cubic stochastic matrix
• digraph
• trigraph

AMS Subject Classifications:

• 17D92
• 05C25
• 17A60
• 16W99

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

This work is partially supported by the Spanish Ministerio de Economía y Competitividad [MTM2013-45588-C3-2-P].