Head, Tom The topological structure of the space of unending paths of a graph. (English) Zbl 0645.05037 Combinatorics, graph theory, and computing, Proc. 18th Southeast. Conf., Boca Raton/Fl. 1987, Congr. Numerantium 60, 131-140 (1987). Summary: [For the entire collection see Zbl 0638.00009.] Let G be a finite rooted directed multigraph. With each such G is associated an algorithmically constructed graph CF(G) of the same type. It is demonstrated that the spaces of unending paths in two finite rooted directed multigraphs G and G’ are homeomorphic if and only if the graphs CF(G) and CF(G’) are isomorphic. It is shown that a topological space is homeomorphic with the space of unending paths in such a graph G if and only if it is compact, zero-dimensional, metrizable and of finite type. Cited in 2 Documents MSC: 05C10 Planar graphs; geometric and topological aspects of graph theory 05C38 Paths and cycles Keywords:finite rooted directed multigraph; spaces of unending paths Citations:Zbl 0638.00009 PDF BibTeX XML OpenURL