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Two graph r isomorphic iff they have :

1. Same no of edges

2. Same no of vertices

3. Same no of particular length (i.e. 3 length , 4 length,.....) cycle..
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1)Both graphs have equal no of vertices(10).

2)Both graphs have equal no of edges(15).

3)Both graphs have same degree sequence. 3,3,3,3,3,3,3,3,3,3

4)Each vertex in both graphs is connected to other 3 vertices of degree three

so there neighboring vertices degree is also same in both graphs(this cover the concepts of same pairs of cycles).

Hence both graph are isomorphic.
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