Below are three sequences of length10. One of the sequences cannot be the degree

Question

Below are three sequences of length10. One of the sequences cannot be the degree sequence (see exercise 33) of any graph. Identify it and say why. For each of the other two, say why (if you have enough information) a connected graph with that degree sequence

• is denitely hamiltonian/cannot be hamiltonian;

• is denitely eulerian/cannot be eulerian;

• is denitely a tree/cannot be a tree;and

• is denitely planar/cannot be planar.

(From Excercise 33)

a) n = 10: (4,4,2,2,1,1,1,1,1,1)

b) n = 9: (8,8,8,6,4,4,4,4,4)

c) n = 7: (5,4,4,3,2,1,0)

d) n = 10: (7,7,6,6,6,6,5,5,5,5)

e) n = 6: (5,4,3,2,2,2)

Explanation / Answer

Below are three sequences of length10. One of the sequences cannot be the degree

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