Evolution algebras and graphs

By Alberto Elduque, Alicia Labra. 2013

88 citations recorded by the source corpus.

A digraph is attached to any evolution algebra. This graph leads to some new purely algebraic results on this class of algebras and allows for some new natural proofs of known results. Nilpotency of an evolution algebra will be proved to be equivalent to the nonexistence of oriented cycles in the graph. Besides, the automorphism group of any evolution algebra $E$ with $E=E^2$ will be shown to be always finite.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/108240cab110b644e166f567998a9b458a3f442f