Prove that x(G) x (G) n(G), use this to prove that x (G) + x(G)...

 

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Prove that x(G) x (G) ≥ n(G), use this to prove that x (G) + x(G) ≥ 2√n(G), and provide a construction achieving these bounds whenever √n(G) is an integer. Prove that x(G) x (G) ≥ n(G), use this to prove that x (G) + x(G) ≥ 2√n(G), and provide a construction achieving these bounds whenever √n(G) is an integer.