Prove that for n ⩾ 2 there are exactly two n-vertex graphs with n − 1...

Prove that for n ⩾ 2 there are exactly two n-vertex graphs with n − 1 distinct degrees (up to isomorphism). The other answers on the website are incorrect.

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Colby Messinger answered 1 year ago

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Prove that for all integers n ≥ 2, the number p(n) − p(n − 1) is equal to the number of partitions of n in which the two largest parts are equal.

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Prove that the number of partitions of n into parts of size 1 and 2 is...

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Discrete Mathematics A tree contains 1 vertex of degree 2, 1 vertex of degree 3, 1 vertex of degree 4, 11 leaves and the remaining vertices have degree 3. Find the total number of vertices. Sketch two non-isomorphic trees statisfying the above mentioned conditions.

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