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We prove two isomorphism-invariance theorems for groupoids associated withultragraphs. These theorems characterize ultragraphs for which the topologicalfull group of an associated groupoid is an isomorphism invariant. These resultsextend those of graph groupoids to ultragraph groupoids while providing anotherconcrete example where the topological full group of a groupoid is a completeisomorphism invariant.

Topological full groups of ultragraph groupoids as an isomorphism invariant