Embedding Higman-Thompson groups of unfolding trees into the Leavitt path algebras

The isomorphism problem of regular Higman-Thompson groups was solved in arXiv:1006.1759, via embedding it into the Leavitt algebra. In this paper, we will expand these results to embed the Higman-Thompson groups of unfolding trees of directed graphs into the Leavitt path algebra. This embedding allows us to show that any isomorphism of rooted Leavitt path algebras induces an isomorphism between Higman-Thompson groups.