Question: Let G1, G2 be two loop-free connected undirected graphs. If G1, G2 are homeomorphic, prove that (a) G1, G2 have the same number of vertices

Let G1, G2 be two loop-free connected undirected graphs. If G1, G2 are homeomorphic, prove that (a) G1, G2 have the same number of vertices of odd degree; (b) G1 has an Euler trail if and only if G2 has an Euler trail; and (c) G1 has an Euler circuit if and only if G2 has an Euler circuit.

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