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Find several perfect matchings of the petersen graph

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Reference no: EM131586978

Question: 1. Find several perfect matchings of the Petersen graph.

2. Find a closed form for the recurrence an = an-1 +4an-2 -4an-3 and initial values a0 = 4, a1 = 2, a2 = 10.

3. Consider a function on the real numbers defined by f(1) = q and f(a+b) = f(a)· f(b) for all real numbers a,b.

(a) Prove by induction that f(n) = qn for all n ∈ N.

(b) Show that if q ≠ 0, then f(0) = 1.

Reference no: EM131586978

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