Question 1 Let G = (V, E) be a graph. Check all true statements. The number of e

Question

Question 1

Let G = (V, E) be a graph. Check all true statements.

The number of even-degree vertices must be even.

The sum of degrees of all vertices must be even.

The number of odd-degree vertices must be odd.

The number of odd-degree vertices must be even.

The number of even-degree vertices must be odd.

The number of even-degree vertices must be even.

The sum of degrees of all vertices must be even.

The number of odd-degree vertices must be odd.

The number of odd-degree vertices must be even.

The number of even-degree vertices must be odd.

Explanation / Answer

Solution: Statement 2 is true because, In any graph, the sum of the degrees of all vertices is equal to twice the number of edges.

Statement 4 is true. it is standard proof, you may look at any standard text book on Graph theory.

Statement 1 is also true, based on the above results.

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