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May 5, 2026Mathematics2 citationsOpen Access

On the Hitting Time Index of Broom Graphs

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JPJosé Luis Palacios

Key Points

  • The aim is to derive closed-form formulas for the hitting time index of broom graphs based on random walk properties.
  • Utilized the formula for commute time of random walks between two vertices.
  • Calculated effective resistance for broom graphs to establish relationships.
  • Extended previously known results in the field.
  • Closed-form formulas for hitting time index are provided for specific broom graph families.
  • Results extend findings reported by He et al. with clearer mathematical expressions.

Abstract

A broom graph is a linear graph with some pendant vertices attached to one of its ends. Using the formula for the commute time of the random walk between two vertices of the graph, which is given in terms of the effective resistance between the vertices, we find closed-form formulas for the hitting time index of some families of broom graphs, extending results found by He et al.

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Cite This Study

José Luis Palacios (2026) studied this question.

synapsesocial.com/papers/69f9892215588823dae18000https://doi.org/10.3390/math14091508
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