Properties of the gradings on ultragraph algebras via the underlying combinatorics

There are two established gradings on Leavitt path algebras associated with ultragraphs, namely the grading by integers group and free edges. In this paper, we characterize properties of these in terms underlying combinatorial ultragraphs. More precisely, when strong or epsilon-strong. The results regarding edges new also context graphs. Finally, describe relationship between strongness integer an ultragraph algebra saturation gauge action corresponding C*-algebra.