Use the theorem that relates the sum of degrees to the number of edges to determine the number of edges in the graph.
-A graph with 8 vertices, one of degree 4, three of degree 2, and four of degree 1.
A)6 edges
B)7 edges
C)14 edges
D)5 edges

Question

Quizplus · Accepted Answer

The theorem that relates the sum of degrees to the number of edges in a graph states that the sum of the degrees of all vertices in a graph is twice the number of edges. For this graph, the sum of the degrees is 4 + 3(2) + 4(1) = 4 + 6 + 4 = 14. Therefore, the number of edges is 14 / 2 = 7.

Use the Theorem That Relates the Sum of Degrees to the Number