S-Graphicable Algebras and Specific Graph Families

Abstract

This paper presents new developments in the relationship between S-graphicable algebras and graphs. Several general algebraic properties of S-graphicable evolution algebras are established, including characterizations of the annihilator, idempotent elements, and evolution subalgebras. It is also shown that S-graphicable algebras are nonsolvable, and several results concerning their perfectness are provided. In addition, new families of S-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 S-graphicable and, if so, to construct its associated graph.

Es la versión aceptada del articulo. Se puede consultar la versión final en https://doi.org/10.1002/mma.70534