2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100836We investigate the ideal structures of the C^*-algebras arising from topological graphs. We give the complete description of ideals of such C^*-algebras which are invariant under the so-called gauge action, and give the condition on topological graphs so that all ideals are invariant under the gauge action. We get conditions for our C^*-algebras to be simple, prime or primitive. We completely determine the prime ideals, and show that most of them are primitive. Finally, we construct a discrete graph such that the associated C^*-algebra is prime but not primitive.47 pages, typos corrected, Sections 11 and 12 ChangedOperator AlgebrasDynamical SystemsPrimary 46L05; Secondary 46L55, 37B99text