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**Concept: **

By using handshaking theorem of graph theory, the sum of degree of all the vertices in a tree is equal to twice the number of edges in a graph.

**Formula:**

\(\mathop \sum \limits_{i = 1}^{i = n} {d_i} = 2 \times e\)

where d_{i} is the degree of vertex i and e is the total number of edges in a graph

**Calculation:**

For a tree,

number of edges = e = n – 1

\(\mathop \sum \limits_{i = 1}^{i = n} {d_i} = 2\left( {n - 1} \right)\)

\(\mathop \sum \limits_{i = 1}^{i = n} {d_i} = 2\left( {10 - 1} \right) = 18\)

sum of the degrees of all the vertices in T is 18

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