Question

How many cycles are there in a wheel graph of order 5?

(a) 6

(b) 10

(c) 25

(d) 7

I have been asked this question during an online interview.

This interesting question is from Trees in division Trees of Discrete Mathematics

Answer 1

Right option is (d) 7

To explain: In a cycle of a graph G if we join all the vertices to the centre point, then that graph is called a wheel graph. There is always a Hamiltonian cycle in a wheel graph and there are n^2-3n+3 cycles. So, for order 5 the answer should be 7.