theorem Th9: :: GLPACY00:5

for G2 being _Graph
for v, e, w being object
for v2 being Vertex of G2
for G1 being addAdjVertex of G2,v,e,w
for v1 being Vertex of G1 st v1 <> v & v1 <> w & v1 = v2 holds
( v1 .edgesIn() = v2 .edgesIn() & v1 .inDegree() = v2 .inDegree() & v1 .edgesOut() = v2 .edgesOut() & v1 .outDegree() = v2 .outDegree() & v1 .edgesInOut() = v2 .edgesInOut() & v1 .degree() = v2 .degree() )