Show that the two graphs are isomorphic (Narsingh Deo)

Question

Show that the two graphs are isomorphic

Comments

Label vertex in one of the graph, now in the second graph pick any vertex and labelled it 1 and labelled all neighbours accordingly, now repeat this process for another vertex in the end if no vertex has more them one labelled and all vertex have exactly one label then you are done

Answer 1

1) Number of vertices are same in both.

2) Number of edges are same in both.

3) Each vertex has degree=4 in both.

Now place 7 vertices using the same structure as in original graph and mark the numbering in clockwise order as: $\left \{ 1,6,4,2,7,5,3 \right \}$.

Using graph (b) (the numbered graph in above pic), place edges between the newly placed vertices.

NOTE: The edges are to be placed using graph (b).

You can clearly get the original graph.
Hence both are ISOMORPHIC.

Answer 2

1)Both graph has 7 vertices.

2)Both graphs have 13 edges.

3)Their degree sequence is same.

and each vertex is both graphs have degree 4 hence they are isomorphic in nature.

Comments

both graph having $14$ edges