The topological structure of the space of unending paths of a graph. (English) Zbl 0645.05037

Head, Tom

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.

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