12 13 14 plz give me some step this is review question for m

#12, 13, 14.

plz give me some step, this is review question for my exam, i need help.

thank you very much!

Solution

Question 12)

G2 and G3 exhibit isomorphism. There is no other pair which exhibits isomorphism.

The reason why G2 and G3 are isomorphic is that if we flip the middle rectangle in G2 around the top edge of rectangle, then G2 will get converted to G3. Therefore, G2 and G3 are basically the same graphs, they have just been shown in different ways.

No other pair is isomorphic because G1, G3 (same as G2) and G4 are plannar graphs.

And:

G1 contains 2 rectangles, 2 triangles and 1 pentagon

G3 contains 2 pentagons, 2 rectangles and 1 triangle

G4 contains 5 rectangles.

Therefore, none of G1, G3 and G4 make an isomorphic pair. Since G2 is same as G3, hence, (G2, G3) is the only isomorphic pair