Question

Draw two non-isomorphic 7-vertex, 7-edge simple graphs with the same
degree sequence.
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Answer 1

Step-by-step explanation:

Let G1 be a graph on 7 vertices that is a cycle. Then every vertex has degree 2. Let G2 be a graph on the same 7 vertices that consists of precisely a vertex-disjoint 4-cycle and 3-cycle.

Then G1 and G2 have the same degree sequence; every vertex in G1 has degree 2, and every vertex in G2 also has degree 2. But are G1 and G2 isomorphic?

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Divyashree 14