theorem :: GLIB_012:116

for G1 being simple _Graph
for G2 being GraphComplement of G1
for v1 being Vertex of G1
for v2 being Vertex of G2 st v1 = v2 & G1 .order() = 2 holds
( ( v1 is endvertex implies v2 is isolated ) & ( v2 is isolated implies v1 is endvertex ) & ( v1 is isolated implies v2 is endvertex ) & ( v2 is endvertex implies v1 is isolated ) )