Local Complementations of Simple and Directed Graphs

The operation of local complementation was introduced by A. Bouchet while studying Euler cycles in 4-regular graphs and graphs of chord intersections. This paper surveys some recent results on local complementations.The notions of local complementation and local equivalence are generalized to the case of directed graphs. Several theorems analogous to those obtained earlier for simple graphs are proved for directed graphs. Among other results, the conjecture of A. Bouchet on simple graphs isomorphic to their local equivalents is proved.