(Question 3) Let n 2 2 be an integer. Let Gn be the graph defined as follows: the vertex set of Gn is the set of all integer compositions of n, and two compositions a and B in V (Gn) are adjacent if there is a part a of a and a part b of B such that a = b. For instance (1, 1, 3) and (4, 1) are adjacent in G5 since both compositions contain a part equal to 1. How many components does Gn have? Prove your claim. %3D 2:36 pm

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