Number of spanning trees in a wheel graph with two identified vertices via hitting times

Fuente: arXiv
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Main Authors: Tamura, Shunya, Tanaka, Yuuho
Format: Preprint
Published: 2025
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author Tamura, Shunya
Tanaka, Yuuho
author_facet Tamura, Shunya
Tanaka, Yuuho
contents In this paper, we provide an exact formula for the average hitting times in a wheel graph $W_{N+1}$ 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.
format Preprint
id arxiv_https___arxiv_org_abs_2502_01965
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Number of spanning trees in a wheel graph with two identified vertices via hitting times
Tamura, Shunya
Tanaka, Yuuho
Combinatorics
In this paper, we provide an exact formula for the average hitting times in a wheel graph $W_{N+1}$ 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.
title Number of spanning trees in a wheel graph with two identified vertices via hitting times
topic Combinatorics
url https://arxiv.org/abs/2502.01965