Test2Solution

# Test2Solution - 1 a does not exist(cant have a vertex of...

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1. a) does not exist (can’t have a vertex of degree 6) b) Eulerian or Hamiltonian. Eulerian is that all are even degree. Hamiltonian requires Ore’s Theorem or other explanation, hence expect Eulerian for this part. c) Eulerian or Hamiltonian. Eulerian is that all are even degree. Hamiltonian uses Dirac’s theorem. Expect Hamiltonian for this one. d) Tree as degree sum = 16 = 2(n-1) e) Disconnected as degree sum < 16 2. a) D_6 = 6! (1- 1/1! + 1/2! – 1/3! + 1/4! +1/5! – 1/6!) is acceptable. Simply looking for an indication that you used this formula or an alternate formulation of it. If you messed up the algebra in simplifying this expression, I instructed the TA’s to still give full credit. b) (10 choose 7) * D_7 c) (8 choose 3) * D_3 + (8 choose 2) * D_2 + 0 + 1 3. a) (15 + 3 -1 choose 15) = (17 choose 15) b) (11 + 3 -1 choose 11) = (13 choose 11) c) (5 + 2 -1 choose 5) * (10 + 1 -1 choose 10) = (6 choose 5) * (10 choose 10) = 6 * 1 4. 0 2 inf 1 inf inf 1

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## This note was uploaded on 11/08/2009 for the course MATH 2602 taught by Professor Costello during the Spring '09 term at Georgia Tech.

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Test2Solution - 1 a does not exist(cant have a vertex of...

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