TITLE: what are the applications of the isomorphic graphs?
QUESTION [9 upvotes]: While studying data structures i was told my instructor that even i am given 3 hour/30 days/3 years to find out whether two graphs are isomorphic or not, it is  very very complex and even after spending this much amount of time i will not able to figure out clearly whether the given two graphs are isomorphic or not. It is NP-complete problem.
So i got the curiosity that why i am studying it then. What could be the possible applications of such isomorphic graphs which can be solved ?

REPLY [5 votes]: A good example is the perturbative expansion of Feynman's path integral by summing over Feynman diagrams. This is an infinite series, each stage of which is parameterized by a finite sum over isomorphism classes of certain kinds of graphs. Writing down all isomorphism classes of graphs with certain data requires being able to tell if two graphs are isomorphic.