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There are two established gradings on Leavitt path algebras associated withultragraphs, namely the grading by the integers group and the grading by thefree group on the edges. In this paper, we characterize properties of thesegradings in terms of the underlying combinatorial properties of theultragraphs. More precisely, we characterize when the gradings are strong orepsilon-strong. The results regarding the free group on the edges are new alsoin the context of Leavitt path algebras of graphs. Finally, we also describethe relation between the strongness of the integer grading on an ultragraphLeavitt path algebra and the saturation of the gauge action associated with thecorresponding ultragraph C*-algebra.

Properties of the gradings on ultragraph algebras via the underlying combinatorics