theorem :: GLIB_012:58

for G1 being _Graph
for G2 being DLGraphComplement of G1
for v1 being Vertex of G1
for v2 being Vertex of G2 st v1 = v2 holds
( ( v1 is isolated implies not v2 is isolated ) & ( v1 is endvertex implies not v2 is endvertex ) )