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On Steiner degree distance of trees

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  • Gutman, Ivan

Abstract

Let G be a connected graph, and u, v, w its vertices. By du is denoted the degree of the vertex u, by d(u, v) the (ordinary) distance of the vertices u and v, and by d(u, v, w) the Steiner distance of u, v, w. The degree distance DD of G is defined as the sum of terms [du+dv]d(u,v) over all pairs of vertices of G. As early as in the 1990s, a linear relation was discovered between DD of trees and the Wiener index. We now consider SDD, the Steiner–distance generalization of DD, defined as the sum of terms [du+dv+dw]d(u,v,w) over all triples of vertices of G. Also in this case, a linear relation between SDD and the Wiener index could be established.

Suggested Citation

  • Gutman, Ivan, 2016. "On Steiner degree distance of trees," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 163-167.
    • Handle: RePEc:eee:apmaco:v:283:y:2016:i:c:p:163-167
    DOI: 10.1016/j.amc.2016.02.038
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    References listed on IDEAS

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    1. Zhang, Yanhong & Hu, Yumei, 2016. "The Nordhaus–Gaddum-type inequality for the Wiener polarity index," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 880-884.
    2. Das, Kinkar Ch. & Gutman, Ivan & Nadjafi–Arani, Mohammad J., 2015. "Relations between distance–based and degree–based topological indices," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 142-147.
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    Cited by:

    1. 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.
    2. Hongfang Liu & Jinxia Liang & Yuhu Liu & Kinkar Chandra Das, 2023. "A Combinatorial Approach to Study the Nordhaus–Guddum-Type Results for Steiner Degree Distance," Mathematics, MDPI, vol. 11(3), pages 1-19, February.
    3. 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).
    4. Tratnik, Niko, 2018. "On the Steiner hyper-Wiener index of a graph," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 360-371.
    5. Wu, Xiaoxia & Zhang, Lianzhu & Chen, Haiyan, 2017. "Spanning trees and recurrent configurations of a graph," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 25-30.

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