Question

If the number of vertices of a chromatic polynomial PG is 56, what is the degree of PG?

(a) 344

(b) 73

(c) 265

(d) 56

This question was posed to me by my school principal while I was bunking the class.

This intriguing question comes from Planarity, Degree and Coloring of Graph in section Graphs of Discrete Mathematics

Answer 1

The correct answer is (d) 56

The explanation is: The chromatic polynomial PG of a graph G is a polynomial in which every natural number k returns the number PG(k) of k-colorings of G. Since, the degree of PG is equal to the number of vertices of G, the required answer is 56.