According to the following graphs below, they are isomorphic. The matching pairs of the isomorphic graphs below are:
a - 7
b - 3
c - 5
d - 4
e - 1
f - 2
g - 6
However, I have the following:
a - 4
b - 3
c - 5
d - 7
e - 1
f - 2
g - 6
Unless I made a mistake. Thank you.
Also, is it possible to use compare adjacent matrices of each graph to see if Isomorphism exists (To be able to check in a faster rate rather than use trial and error)? Thank you
On
In general: yes, this can happen. The question is, did it happen here?
You have found an isomorphism between the first graph and the second graph, but with different labels. Remembering that isomorphism is an equivalence relation, the question is: is there an isomorphism between the second graph and the second graph with different labels that turns your differently-labelled version into the correct version?
Yes, this happens. Your solution is correct. There can generally be more than one isomorphism between different graphs, just as there can be more than one bijection between two sets, or isomorphism between two groups, or homeomorphism between two topological spaces.