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Extremal trees of a given degree sequence or segment sequence with respect to average Steiner 3-eccentricity

Author

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  • Li, Shuchao
  • Liu, Xin
  • Sun, Wanting
  • Yan, Lixia

Abstract

The Steiner k-eccentricity of a vertex in a graph G is the maximum Steiner distance over all k-subsets containing the vertex. The average Steiner k-eccentricity of G is the mean value of all vertices’ Steiner k-eccentricities in G. Let Tn be the set of all n-vertex trees, Tn,Δ be the set of n-vertex trees with maximum degree Δ, Tn,Δk be the set of n-vertex trees with exactly k vertices of a given maximum degree Δ, and let MTnk be the set of n-vertex trees with exactly k vertices of maximum degree. In this paper, we first determine the sharp upper bound on the average Steiner 3-eccentricity of n-vertex trees with a given degree sequence. The corresponding extremal graphs are characterized. Consequently, together with majorization theory, all graphs among Tn,Δk (resp. Tn,Δ,MTnk,Tn) having the maximum average Steiner 3-eccentricity are identified. Then we characterize the unique n-vertex tree with a given segment sequence having the minimum average Steiner 3-eccentricity. Finally, we determine all n-vertex trees with a given number of segments having the minimum average Steiner 3-eccentricity.

Suggested Citation

  • Li, Shuchao & Liu, Xin & Sun, Wanting & Yan, Lixia, 2023. "Extremal trees of a given degree sequence or segment sequence with respect to average Steiner 3-eccentricity," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    • Handle: RePEc:eee:apmaco:v:438:y:2023:i:c:s0096300322006300
    DOI: 10.1016/j.amc.2022.127556
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    References listed on IDEAS

    as
    1. Deng, Kecai & Li, Shuchao, 2021. "On the extremal values for the Mostar index of trees with given degree sequence," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    2. Gutman, Ivan, 2016. "On Steiner degree distance of trees," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 163-167.
    3. Zhang, Jie & Wang, Hua & Zhang, Xiao-Dong, 2019. "The Steiner Wiener index of trees with a given segment sequence," Applied Mathematics and Computation, Elsevier, vol. 344, pages 20-29.
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