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 10 vertices, three of degree 5, three of degree 3, two of degree 2, and two of degree 1.
A)18 edges
B)12 edges
C)11 edges
D)15 edges

Question

Quizplus · Accepted Answer

The sum of the degrees of all vertices in a graph is twice the number of edges. For this graph, the sum of degrees = (3*5) + (3*3) + (2*2) + (2*1) = 15 + 9 + 4 + 2 = 30. Since the sum of the degrees is 30, the number of edges = 30 / 2 = 15.

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