Question

What is the grade of a  planar graph consisting of 8 vertices and 15 edges?

(a) 30

(b) 15

(c) 45

(d) 106

The question was posed to me in an interview for job.

This interesting question is from Isomorphism in Graphs in division Graphs of Discrete Mathematics

Answer 1

Right answer is (a) 30

The explanation is: If G is a planar graph with n vertices and m edges then r(G) = 2m i.e. the grade or rank of G is equal to the twofold of the number of edges in G. So, the rank of the graph is 2*15=30 having 8 vertices and 15 edges.