Isomorphisms and Homeomorphisms of a Class of Graphs and Spaces

We solve the isomorphism problem for the whole class of Lins-Mandel gems (graphs encoded manifolds). We also present certain homeomorphisms of branched cyclic coverings of two-bridge hyperbolic links. As a consequence, we prove that, in in a wide subset of interesting cases, the isomorphism conditions for Lins-Mandel gems are equivalent to the homeomorphism conditions for the encoded 3-manifolds.