Leaves of a degree-3 tree

MediumProgramming & DSA~4m

A tree (connected, acyclic, undirected) has $10$ vertices. Every vertex is either a leaf (degree $1$ ) or an internal vertex of degree exactly $3$ . How many leaves does it have?

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A tree on $V$ vertices has $V-1$ edges; the handshake lemma says the degrees sum to $2E$ .
Let $L$ leaves (deg 1) and $10-L$ internal (deg 3): solve $L + 3(10-L) = 2(10-1)$ .

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Leaves of a degree-3 tree

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