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In this article, we introduce a relation including ideals of an evolutionalgebra and hereditary subsets of vertices of its associated graph andestablish some properties among them. This relation allows us to determinemaximal ideals and ideals having the absorption property of an evolutionalgebra in terms of its associated graph. We also define a couple oforder-preserving maps, one from the sets of ideals of an evolution algebra tothat of hereditary subsets of the corresponding graph, and the other in thereverse direction. Conveniently restricted to the set of absorption ideals andto the set of hereditary saturated subsets, this is a monotone Galoisconnection. According to the graph, we characterize arbitrary dimensionalfinitely-generated (as algebras) evolution algebras under certain restrictionsof its graph. Furthermore, the simplicity of finitely-generated perfectevolution algebras is described on the basis of the simplicity of the graph.

Connecting ideals in evolution algebras with hereditary subsets of its associated graph