In a simple graph, the number of edges is equal to twice the sum of the degrees of the vertices.Group of answer choicesFalseTrue

Answer

The statement "In a simple graph, the number of edges is equal to twice the sum of the degrees of the vertices" is False.

Explanation

According to the Handshaking Lemma in graph theory, the sum of the degrees of all vertices in a graph is equal to twice the number of edges. The proper relationship is given by:

$\sum_{v \in V} \deg(v) = 2E$

where:

• $E$ is the number of edges,
• $\deg(v)$ represents the degree of vertex $v$, and
• $V$ is the set of vertices in the graph.

Thus, the number of edges is half the sum of the degrees of the vertices:

$E = \frac{1}{2} \sum_{v \in V} \deg(v)$

Final Answer

False