
theorem
  for G being _Graph holds G is self-Dcomplementary iff
    ex H being DGraphComplement of G st H is G-Disomorphic
proof
  let G be _Graph;
  hereby
    assume A1: G is self-Dcomplementary;
    reconsider H = the DGraphComplement of G as DGraphComplement of G;
    take H;
    thus H is G-Disomorphic by A1;
  end;
  given H0 being DGraphComplement of G such that
    A2: H0 is G-Disomorphic;
  let H be DGraphComplement of G;
  H is H0-Disomorphic by Th85;
  hence H is G-Disomorphic by A2;
end;
