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Combinatorics
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answerhappygod
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Combinatorics
Combinatorics
5. (a) For n € N, find the number of 1-regular graphs G with V(G) = {1,2,..., 2n}. Show that it is equal to 2-" (2n)². (b) For n € N, find the number of 2-regular graphs G with V(G) = {1,2,..., 3n} such that every cycle in G has length 3. Show that it is equal to 6-(3n)²n
5. (a) For n € N, find the number of 1-regular graphs G with V(G) = {1,2,..., 2n}. Show that it is equal to 2-" (2n)². (b) For n € N, find the number of 2-regular graphs G with V(G) = {1,2,..., 3n} such that every cycle in G has length 3. Show that it is equal to 6-(3n)²n