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  3. let s = {a, b, c}. draw a graph whose vertex set i

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

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Advance Math

Let S = {a, b, c}. Draw a graph whose vertex set is P(S) and forwhich the subsets A and B of S are adjacent if and only if A ⊂ Band |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 ofthe matching.

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

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