## Bee_see one year ago Are the following pairs of graphs isomorphic? If they are isomorphic, label the vertices to show an isomorphism. If they are not isomorphic, explain why not; specifically, find a graph property that is not shared by both graphs. It suffices for this problem to merely state the graph properties–you do not need to prove rigorously that they hold.

1. Bee_see

2. anonymous

At first I thought it said Islamophobic so I was getting my caps lock ready|dw:1440778755730:dw|

3. freckles

looks like we need to consider the degree of the nods |dw:1440782933158:dw|

4. freckles

\[\deg(A)=3 \\ \deg(B)=3 \\ \deg(C)=3 \\ \deg(D)=3 \\ \deg(E)=2 \\ \deg(F)=2 \\ \deg(G)=2 \\ \deg(H)=2 \\ \deg(I)=4 \\ ... \\ \deg(1)=3 \\ \deg(2)=3 \\ \deg(3)=3 \\ \deg(4)=3 \\ \deg(5)=2 \\ \deg(6)=2 \\ \deg(7)=2 \\ \deg(8)=2 \\ \deg(9)=4\]

5. freckles

so we have degree numbers match up

6. freckles

that is probably not enough information like if the degree things didn't match up we could say it isn't isomorphic but I think we might need a bit more now

7. Bee_see

Ok.

8. freckles

|dw:1440783764768:dw| looks like these graphs would be the same if you rotate the inner square and make that inner square thing into an X

9. Bee_see

I don't think the professor would like to rotate it...

10. freckles

|dw:1440783799919:dw| hmm but this shows there is an edge going from A to E and we didn't previously have that

11. freckles

so mapping A to 1 and E to 5 wouldn't work because A to E are not connected while 1 to 5 is

12. freckles

so appears these graphs are not isomorphic

13. Bee_see

why exactly did you rotate the square?

14. freckles

I was trying to see if the graphs would be the same if I reconstructed the first to try to look like the second but in reconstruction I noticed the information about the edges there

15. freckles

something easier for you might be to compare the number of edges from each

16. Bee_see

don't both have 12 edges though?

17. freckles

|dw:1440784272471:dw| nevermind