Let S = {a, b, c}. Draw a graph whose vertex set is P(S) and for...

Let S = {a, b, c}. Draw a graph whose vertex set is P(S) and for which the subsets A and B of S are adjacent if and only if A ⊂ B and |A| = |B| − 1.

(a) How many vertices and edges does this graph have?

(b) Can you name this graph?

(c) Is this graph connected?

(d) Does it have a perfect matching? If yes, draw a sketch of the matching.

(e) Does it have a Hamiltonian cycle? If yes, draw a sketch of the cycle.

Expert Solution

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Colby Messinger answered 2 years ago

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