Two graphs which contain the same number of graph vertices connected in the same way are said to be isomorphic. Formally, two graphs G and H with graph vertices Vn={1,2,...,n} are said to be isomorphic if there is a permutation p of Vn such that {u,v} is in the set of graph edges E(G) iff {p(u),p(v)} is in the set of graph edges E(H).

To find out if given two graph are isomorphic or not please check the following link

http://www.ms.uky.edu/~csima/ma111/GraphsLecture2.pdf

and also check the following video