for G1, G2 being _Graph
for F being PGraphMapping of G1,G2 st F is isomorphism holds
( ( G1 is acyclic implies G2 is acyclic ) & ( G2 is acyclic implies G1 is acyclic ) & ( G1 is chordal implies G2 is chordal ) & ( G2 is chordal implies G1 is chordal ) & ( G1 is connected implies G2 is connected ) & ( G2 is connected implies G1 is connected ) )