
theorem Th112:
  for G1 being _Graph, G2 being GraphComplement of G1 holds
    (G1 is _trivial iff G2 is _trivial)
proof
  let G1 be _Graph, G2 be GraphComplement of G1;
  hereby
    assume G1 is _trivial;
    then 1 = G1.order() by GLIB_000:26
      .= G2.order() by Th111;
    hence G2 is _trivial by GLIB_000:26;
  end;
  hereby
    assume G2 is _trivial;
    then 1 = G2.order() by GLIB_000:26
      .= G1.order() by Th111;
    hence G1 is _trivial by GLIB_000:26;
  end;
end;
