Homeomorphism (graph theory)

In graph theory, two graphs and are homeomorphic if there is a graph isomorphism from some subdivision of to some subdivision of . If the edges of a graph are thought of as lines drawn from one vertex to another (as they are usually depicted in diagrams), then two graphs are homeomorphic to each other in the graph-theoretic sense precisely if their diagrams are homeomorphic in the topological sense.[1]

  1. ^ Archdeacon, Dan (1996), "Topological graph theory: a survey", Surveys in graph theory (San Francisco, CA, 1995), Congressus Numerantium, vol. 115, pp. 5–54, CiteSeerX 10.1.1.28.1728, MR 1411236, The name arises because and are homeomorphic as graphs if and only if they are homeomorphic as topological spaces