If a graph has 8 vertices and 12 edges, then the degree of each vertex in the graph is:a.3b.6c.12d.10
Question
If a graph has 8 vertices and 12 edges, then the degree of each vertex in the graph is:
- a. 3
- b. 6
- c. 12
- d. 10
Solution
The degree of a vertex in a graph is the number of edges connected to it. In a simple graph, the sum of the degrees of all vertices is equal to twice the number of edges. This is known as the Handshaking Lemma.
Given that the graph has 8 vertices and 12 edges, we can use the Handshaking Lemma to find the sum of the degrees of all vertices:
Sum of degrees = 2 * number of edges Sum of degrees = 2 * 12 = 24
Since there are 8 vertices in the graph, the degree of each vertex is:
Degree of each vertex = Sum of degrees / number of vertices Degree of each vertex = 24 / 8 = 3
So, the degree of each vertex in the graph is 3. Therefore, the correct answer is a. 3.
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