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Minimum status of trees with a given degree sequence

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Abstract

The minimum status (or its normalized version called proximity) is a well-known concept in communication network theory. We determine the trees minimizing the minimum status among trees with a given degree sequence, and we show that the trees maximizing the minimum status among trees with a given degree sequence must be caterpillars with specific properties.

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Acknowledgements

The authors thank the editor and the referees for very helpful and constructive comments and suggestions on early versions. This work was supported by National Natural Science Foundation of China (No. 12071158).

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Authors and Affiliations

  1. School of Computer Science, South China Normal University, Guangzhou, 510631, People’s Republic of China

    Haiyan Guo

  2. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, People’s Republic of China

    Bo Zhou

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  1. Haiyan Guo
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Correspondence to Bo Zhou.

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Guo, H., Zhou, B. Minimum status of trees with a given degree sequence. Acta Informatica 60, 1–10 (2023). https://doi.org/10.1007/s00236-022-00416-2

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  • DOI: https://doi.org/10.1007/s00236-022-00416-2