
theorem
  for G being _Graph holds G is self-Lcomplementary iff
    ex H being LGraphComplement of G st H is G-isomorphic
proof
  let G be _Graph;
  hereby
    assume A1: G is self-Lcomplementary;
    reconsider H = the LGraphComplement of G as LGraphComplement of G;
    take H;
    thus H is G-isomorphic by A1;
  end;
  given H0 being LGraphComplement of G such that
    A2: H0 is G-isomorphic;
  let H be LGraphComplement of G;
  H is H0-isomorphic by Th68;
  hence H is G-isomorphic by A2;
end;
