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Define isometric graphs. Show that following graphs are isomorphic.

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**Isometric graphs:**

Two graphs which contain the same number of graph vertices connected in the same way are said to be isomorphic. Formally, two graphs G and H with graph vertices Vn={1,2,...,n} are said to be isomorphic if there is a permutation p of Vn such that {u, v} is in the set of graph edges E(G) iff {p(u),p(v)} is in the set of graph edges E(H).

**Sol:**

Number of vertices: both 5.

Number of edges: both 7.

Degrees of 1 vertices in each of the graph is 2 and rest of the vertices having degree 3.

Connectedness: Each is fully connected.

Number of connected components: Both 1.

Pairs of connected vertices: All correspond.

Number of loops: 0.

Number of parallel edges: 0.

Everything is equal and so the graphs are isomorphic.

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