[Math] I need an example of two non-isomorphic graphs with the same degree sequence.

Question

I'm struggling to find two non-isomorphic graphs with the same degree sequence. The only method I have is trial and error but its yielding no results. Could someone please provide me with one. Or is there a easy, general way of coming up with examples.

NB: There are no no loops and at most one edge between any two vertices.

Answer 1

Let $G_1$ be a graph on 7 vertices that is a cycle. Then every vertex has degree 2. Let $G_2$ be a graph on the same 7 vertices that consists of precisely a vertex-disjoint 4-cycle and 3-cycle.

Then $G_1$ and $G_2$ have the same degree sequence; every vertex in $G_1$ has degree 2, and every vertex in $G_2$ also has degree 2. But are $G_1$ and $G_2$ isomorphic?