Question

An undirected graph has 8 vertices labelled 1, 2, …,8 and 31 edges. Vertices 1, 3, 5, 7 have degree 8 and vertices 2, 4, 6, 8 have degree 7. What is the degree of vertex 8?

(a) 15

(b) 8

(c) 5

(d) 23

This question was addressed to me in unit test.

My question is taken from Graphs topic in portion Graphs of Discrete Mathematics

Answer 1

Correct choice is (b) 8

To explain: Vertices 1, 3, 5, 7 have degree 8 and vertices 2, 4, 6, 8 have degree 7. By definition, sum of degree= 2 * No of edges

Let x = degree of vertex 8

8 + 7 + 8 + 7 + 8 + 7 + 8 + x =  2 * 31

53 + x = 61

x = 8

Hence, degree of vertex 8 is 8.