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Prove that the graph shown in given figure is non-planar

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Reference no: EM131585741

Question: 1. Prove that the graph shown in Figure is non-planar.

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2. The girth of a graph is the length of its smallest cycle. Use this to generalize the statements and proofs of Theorems I and II.

Theorems I: If G is simple, planar, and connected and has at least three vertices, then 3|F(G)| ≤ 2|E(G)|.

Theorems II: If G is simple, planar, connected, and has no 3-cycles, then 4|F(G)| ≤ 2|E(G)|.

Reference no: EM131585741

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