Are Graphs G and H isomorphic? Defend your answer. No b d a f c e u z v y w x Gr

Question

Are Graphs G and H isomorphic? Defend your answer. No

        b           d

a                          f

        c           e

                 u

    z                         v

    y                         w

                 x

Graph G has 4 parallel edges

Graph H 2 parallel edges

Graph G

Initially draw a hexagon with vertices a-b-d-f-e-c-a.

Connect vertices a to f; b to c; d to e.

        b           d

a                          f

        c           e

Graph H

Initially draw a hexagon with vertices u-v-w-x-y-z-u.

Connect vertices u to x; v to y; w to z.

There is no connection in the center.

                 u

    z                         v

    y                         w

                 x

Explanation / Answer

The graph (G) on the left is bipartite (nodes 1,3,5,7 on one side and nodes 2,4,6,8 on the other)

but the graph on the right (H) is not bipartite, it has an odd circuit A,E,G,C,B,A (5 nodes). Also, the

graph on the left is planar, the graph on the right is not.

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