for G2 being _Graph
for v being object
for V being set
for G1 being addAdjVertexAll of G2,v,V st V c= the_Vertices_of G2 & not v in the_Vertices_of G2 holds
( G1 .order() = (G2 .order()) +` 1 & G1 .size() = (G2 .size()) +` (card V) )