=(V, En) 5. Let n1 be an integer and define the graph Gn as follows {0,1}", the set of all binary strings of length...
=(V, En) 5. Let n1 be an integer and define the graph Gn as follows {0,1}", the set of all binary strings of length n. Vn = Two vertices x and y are connected by an edge emu if and only if x and y differs in exactly one position. (a) (4 points) Draw the graph Gn for n = 1,2,3 (b) (4 points) For a general n 2 1, find |Vn and |En (c) (10 points) Prove that for all integer n > 1, G2 has a Hamiltonian cycle
=(V, En) 5. Let n1 be an integer and define the graph Gn as follows {0,1}", the set of all binary strings of length n. Vn = Two vertices x and y are connected by an edge emu if and only if x and y differs in exactly one position. (a) (4 points) Draw the graph Gn for n = 1,2,3 (b) (4 points) For a general n 2 1, find |Vn and |En (c) (10 points) Prove that for all integer n > 1, G2 has a Hamiltonian cycle