The right one has four 4-cycles: 1,2,3,10; 3,4,9,10; 4,5,8,9; 5,6,7,8. I can't find more than c,d,i,h on the left. The one on the right has two disjoint 5-cycles: 1,7,8,9,10; 2,3,4,5,6. On the right I can find more 5-cycles, but none involve a or f. Maybe I'm overlooking some.
Added: Yes, this is a route to show they are not isomorphic. For them to be isomorphic you need the adjacency matrix to be the same once you find the proper mapping. If you can find any property that doesn't match they are not isomorphic. The degrees, number of vertices, number of edges are easy to check, so should be the first step. To make sure, you would say that whatever 3 maps to has to be part of two four-cycles, which also include the thing 10 maps to. Look through all the vertices and see that you can't satisfy this.