Group actions and automorphisms of evolution algebras associated to finite graphs

Given an evolution algebra associated to a connected finite graph $\mathrm{\Gamma }$, we exhibit a free action of the group of symmetries of $\mathrm{\Gamma }$ on the set of automorphisms of the algebra. This allows us to explicitly describe this set and we prove that a sufficient condition for it to be finite is that every automorphism is induced by a graph symmetry. Consequently, we extend a known result about perfect evolution algebras to other families.