theorem Th49: :: GLIB_007:49

for G2 being _Graph
for v being object
for V being set
for G1 being addAdjVertexAll of G2,v,V
for v1, e, v2 being object st V c= the_Vertices_of G2 & not v in the_Vertices_of G2 & v1 <> v & v2 <> v & e Joins v1,v2,G1 holds
e Joins v1,v2,G2