Recognizing locally equivalent graphs

André Bouchet
1993 Discrete Mathematics  
Bouchet, A., Recognizing locally equivalent graphs, Discrete Mathematics 114 (1993) 75-86. To locally complement a simple graph Fat one of its vertices u is to replace the subgraph induced by F on n(o)= {w: w is an edge of F} by the complementary subgraph. Graphs related by a sequence of local complementations are said to be locally equivalent. We describe invariants of locally equivalent graphs and a polynomial algorithm to recognize locally equivalent graphs. An application is given to
more » ... g the number of graphs locally equivalent to a given one.
doi:10.1016/0012-365x(93)90357-y fatcat:hl7xh3favfecxm3pv2foiwgmwy