Abstract:
We introduce a class of inverse semigroups built from directed graphs that we refer to as Leavitt inverse semigroups. These semigroups are closely related to graph inverse semigroups and Leavitt path algebras.We show that two graphs that have isomorphic Leavitt inverse semigroups have isomorphic Leavitt. path algebras and classify graphs that have isomorphic Leavitt inverse semigroups.