Nilpotent evolution algebras of maximal nilindex admit a natural basis in which the structure matrix is strictly upper triangular. In this paper we classify Rota-Baxter operators of weights zero and one on such algebras. We prove that every Rota-Baxter operator is upper triangular with respect to a natural basis. For weight zero, a strong rigidity phenomenon occurs: the operators are diagonal up to possible perturbations supported in the last basis vector. For weight one, a richer structure appears, including both triangular and non-triangular families, with the diagonal entries governed by a rational recurrence relation. Our results provide a complete description of Rota-Baxter operators on nilpotent evolution algebras of maximal nilindex.
Qaralleh et al. (Thu,) studied this question.