Vertex 2‐isomorphism

Abstract

AbstractWhitney's theorem on 2‐isomorphism characterizes the set of graphs having the same cycles as a given graph, where a cycle is regarded as a set of edges. In this paper, vertex 2‐isomorphism is defined and used to prove a vertex analogue of Whitney's theorem. The main theorem states that two connected graphs have the same set of cycles, where a cycle is now regarded as a set of vertices, if and only if one can be obtained from the other by a sequence of simple operations. © 1992 John Wiley & Sons, Inc.