Question

What is the number of vertices in an undirected connected graph with 39 edges, 7 vertices of degree 2, 2 vertices of degree 5 and remaining of degree 6?

(a) 11

(b) 14

(c) 18

(d) 19

This question was addressed to me during an interview for a job.

The query is from Complete and Connected Graphs in division Graphs of Discrete Mathematics

Answer 1

Right choice is (c) 18

For explanation I would say: We know that, sum of degree of all the vertices = 2 * number of edges

2*7 + 5*2 + 6*x = 39*2

x=9

         Number of vertices = 7 + 2 + 9 = 18.