# Whether the attached graphs are isomorphic?

Whether these two graphs are nonisomorphic? They have same number vertices, same regularity, they are cospectral (means: they have same same set of adjacency eigenvalues). I have taken powers of their adjacency matrices and observed that each number in its entries is appearing the same number of times. So whether I could conclude, they are isomorphic!

• There are only 9 vertices, can't you just brute force it? – 5xum Mar 3 '16 at 14:41
• We have $C_4 \dot \cup K_1$ and $K_{1,4}$ are cospectral but not isomorphic. Cospectral is necessary but not sufficient for isomorphism. – ml0105 Mar 3 '16 at 14:52