Transforming trees by successive local complementations
André Bouchet · Journal of Graph Theory · 1988
Abstract A local complementation of a simple graph G at a vertex v consists in replacing the subgraph induced by G on the neighborhood of v by the complementary graph. Two graphs are locally equivalent if they are related by a sequence of local complementations. H. M. Mulder conjectured that any two locally equivalent trees are isomorphic. We prove this conjecture and we characterize those graphs that are locally equivalent to trees.