From the example it looks as if this can be solved linearly, because the structures obviously match. To intuit that the algorithm must be exponential, imagine t

From the example it looks as if this can be solved linearly, because the structures obviously match. To intuit that the algorithm must be exponential, imagine the vertices to be balls on wire. You grab one ball pull it up as the root from which you start to compare. Now it is obvious you have to pick a vertex from the other graph as well to be the root nice from which to begin the comparison, if you pick the wrong one the graphs won't match. So you will have to pick every ball and see if its structure matches. For a tree (a graph without cycles) it's plain to see it's exponential: in the worst case you have to pick each vertex from one graph and then compare its children with the other graph, that's N * N operations. When the graph does have cycles, the problem becomes more complex. How much more complex is what this scientist perhaps put a new upper limit on.