On the average hitting times of the directed wheel

TL;DR

This paper derives explicit formulas for average hitting times of a directed wheel graph with an absorbing vertex, linking these times to Fibonacci and Lucas numbers using elementary methods.

Contribution

It provides a novel explicit formula for hitting times on a directed wheel graph, extending previous work on cycle squares.

Findings

Hitting times are expressed via Fibonacci and Lucas numbers.

Explicit formulas are derived using elementary methods.

The results generalize previous findings on cycle graphs.

Abstract

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.