Number of spanning trees in a wheel graph with two identified vertices via hitting times
Combinatorics
2026-05-13 v1
Abstract
In this paper, we provide an exact formula for the average hitting times in a wheel graph using a combinatorial approach. For this wheel graph, the average hitting times can be expressed using Fibonacci numbers when the number of surrounding vertices is odd and Lucas numbers when it is even. Furthermore, combining the exact formula for the average hitting times with the general formula for the effective resistance of the graph allows determination of the number of spanning trees of the graph with two identified vertices.
Keywords
Cite
@article{arxiv.2502.01965,
title = {Number of spanning trees in a wheel graph with two identified vertices via hitting times},
author = {Shunya Tamura and Yuuho Tanaka},
journal= {arXiv preprint arXiv:2502.01965},
year = {2026}
}