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Minimum Status of Series-Reduced Trees with Given Parameters

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Abstract

For a vertex v of a connected graph G, the status of v is defined as the sum of the distances from v to all other vertices in G. The minimum status of G is the minimum of status of all vertices of G. We give the largest values for the minimum status of series-reduced trees with fixed parameters such as maximum degree, number of pendant vertices, diameter, matching number and domination number, and characterize the unique extremal trees.

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Acknowledgements

The authors thank the referees for constructive comments and suggestions. This work was supported by National Natural Science Foundation of China (Nos. 12071158 and 11801410) and Project Funded by China Postdoctoral Science Foundation (No. 2019M662884).

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Authors and Affiliations

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

    Meiqun Cheng & Bo Zhou

  2. School of Mathematics, South China University of Technology, Guangzhou, 510641, People’s Republic of China

    Hongying Lin

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  1. Meiqun Cheng
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  2. Hongying Lin
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  3. Bo Zhou
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Correspondence to Bo Zhou.

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Cheng, M., Lin, H. & Zhou, B. Minimum Status of Series-Reduced Trees with Given Parameters. Bull Braz Math Soc, New Series 53, 701–720 (2022). https://doi.org/10.1007/s00574-021-00278-1

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