| Summary: | It is broadly known that Lie point symmetries and their subcase, Noether symmetries, can be used as a geometric criterion to select alternative theories of gravity. Here, we use Noether symmetries as a selection criterion to distinguish those models of <inline-formula> <math display="inline"> <semantics> <mrow> <mi>f</mi> <mo>(</mo> <mi>R</mi> <mo>,</mo> <mi>G</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> theory, with <i>R</i> and <i>G</i> being the Ricci and the Gauss−Bonnet scalars respectively, that are invariant under point transformations in a spherically symmetric background. In total, we find ten different forms of <i>f</i> that present symmetries and calculate their invariant quantities, i.e., Noether vector fields. Furthermore, we use these Noether symmetries to find exact spherically symmetric solutions in some of the models of <inline-formula> <math display="inline"> <semantics> <mrow> <mi>f</mi> <mo>(</mo> <mi>R</mi> <mo>,</mo> <mi>G</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> theory.
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