CEBALLOS GONZÁLEZ, MANUEL
No
Math. Meth. Appl. Sci.
Article
Científica
28/01/2026
001672284000001
This paper presents new developments in the relationship between -graphicable algebras and graphs. Several general algebraic properties of -graphicable evolution algebras are established, including characterizations of the annihilator, idempotent elements, and evolution subalgebras. It is also shown that -graphicable algebras are non-solvable, and several results concerning their perfectness are provided. In addition, new families of -graphicable algebras are introduced, each associated with well-known graph types, and the structural relationships among these families are analyzed, revealing significant algebraic connections. Finally, an algorithmic method is presented to determine whether a given evolution algebra is -graphicable and, if so, to construct its associated graph.
derived algebra; evolution algebras; graphicable algebras; graphs