Two graphs are isomorphic if there is a one-to-one correspondence between their vertices that preserves adjacency. This page demonstrates three cases where graphs are not isomorphic for different reasons.
Vertices: 4
Vertices: 5
Degree sequence: 3, 2, 2, 1
Degree sequence: 2, 2, 2, 2
Degree sequence: 3, 3, 3, 3, 2, 2, 2, 2
Number of triangles: 4
Degree sequence: 3, 3, 3, 3, 2, 2, 2, 2
Number of triangles: 0