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This research investigates the maximum hitting time of random walks on unicyclic graphs given their diameter.

April 17, 2026Open Access

Maximum hitting time of random walks on unicyclic graphs with given diameter

Key Points

This research investigates the maximum hitting time of random walks on unicyclic graphs given their diameter.
Analyzed the expected hitting time from one vertex to another in unicyclic graphs.
Derived upper bounds for hitting times based on graph diameter.
Identified extremal graphs that achieve maximum hitting times.
Established an upper bound for the hitting time in unicyclic graphs.
Determined the specific graph structure that corresponds to this maximum value.

Abstract

We explore the extremal problems of the hitting time of unicyclic graphs on n vertices with a given diameter. Let HG (u, v) be the expected hitting time from vertex u to vertex v on a simple graph G. Let? (G) = maxₔₕ{? V (G) }, HG (u, v) be the hitting time of G. In this paper, we obtain the upper bound for the hitting time of unicyclic graphs with a given diameter, and the extremal graph that attached the value is determined.

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Authors

Xiaomin Zhu

Xunda Jiang

Xu Yang

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Filomat

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Institutions

Shanghai Institute of Technology

Shanghai Lixin University of Accounting and Finance

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Maximum hitting time of random walks on unicyclic graphs with given diameter

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Abstract

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