On the average hitting times of the directed wheel

In this paper, following the paper ``On the average hitting times of the squares of cycles,'' we provide an explicit formula for the average hitting times of a simple random walk on a directed graph with $N$ vertices, where the graph consists of a cycle with a single absorbing vertex at its center, using elementary methods. Also, we show that the average hitting times can be expressed in terms of the Fibonacci and Lucas numbers in general.