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Peer-reviewedCC BY 4.0Performance Evaluation

Hitting and cover times of the star graph and the sun graph

  • François Castella
  • Bruno Sericola
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Abstract

We consider the moments and the distribution of the hitting times and cover times of the star graph composed of m arms each of length n. We obtain recurrence relations for the distribution and higher-order moments of both the hitting times of the leaves and the cover times for various initial states. We use the recurrence relations on the moments to analyze the asymptotic behavior of the cover times distribution when the number of arms m, which may depend on the length n of the arms, tends to infinity as n tends to infinity. We call this new graph, composed of an infinite number of arms each of infinite length, the sun graph.

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Cite

BibTeXRIS
BibTeX
@article{castella2026hitting,
  title = {{Hitting and cover times of the star graph and the sun graph}},
  author = {François Castella and Bruno Sericola},
  journal = {Performance Evaluation},
  year = {2026},
  month = oct,
  url = {https://inria.hal.science/hal-05825320v1},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Hitting and cover times of the star graph and the sun graph
AU  - François Castella
AU  - Bruno Sericola
PY  - 2026
DA  - 2026/10/20
JO  - Performance Evaluation
UR  - https://inria.hal.science/hal-05825320v1
AB  - We consider the moments and the distribution of the hitting times and cover times of the star graph composed of m arms each of length n. We obtain recurrence relations for the distribution and higher-order moments of both the hitting times of the leaves and the cover times for various initial states. We use the recurrence relations on the moments to analyze the asymptotic behavior of the cover times distribution when the number of arms m, which may depend on the length n of the arms, tends to infinity as n tends to infinity. We call this new graph, composed of an infinite number of arms each of infinite length, the sun graph.
SN  - 0166-5316
SN  - 1872-745X
ER  -