Let G(V, E) be an undirected graph with l edges. Then the sum of degree of all…
2024
Let G(V, E) be an undirected graph with l edges. Then the sum of degree of all vertices is equal to ______
- A.
2l
- B.
l/2
- C.
l 2
- D.
l
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Correct answer: A
Answer: 2l
Reason: Use the handshake principle for undirected graphs.
Each edge connects two vertices and therefore contributes 1 to the degree of each endpoint.
So every edge contributes a total of 2 to the sum of degrees across all vertices.
With l edges, the total sum of degrees is 2 × l = 2l.
Example: A triangle (3 vertices, 3 edges) has degrees 2 + 2 + 2 = 6, which equals 2 × 3.
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