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Eccentric Distance Sum Of Substitution Tree Networks

Author

Listed:
  • JINMYONG KIM

    (Faculty of Mathematics, Kim Il Sung University, Pyongyang, DPR Korea)

  • MYONGJIN KIM

    (��Pyongyang Software Joint Development Corporation, Pyongyang, DPR Korea)

Abstract

In this paper, we study the eccentric distance sum of substitution tree networks. Calculation of eccentric distance sum naturally involves calculation of average geodesic distance and it is much more complicated. We obtain the asymptotic formulas of average geodesic distance and eccentric distance sum of both symmetric and asymmetric substitution tree networks. Our result on average geodesic distance generalizes the result of [T. Li, K. Jiang and L. Xi, Average distance of self-similar fractal trees, Fractals 26(1) (2018) 1850016.] from symmetric case to asymmetric case. To derive formulas, we investigate the corresponding integrals on self-similar measure and use the self-similarity of distance and measure. For simplicity, we introduce some systematic symbolic assignments and make some assumptions on the graph. We verify that our formulas are correct using the numerical calculation results.

Suggested Citation

  • Jinmyong Kim & Myongjin Kim, 2021. "Eccentric Distance Sum Of Substitution Tree Networks," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(06), pages 1-13, September.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:06:n:s0218348x21501474
    DOI: 10.1142/S0218348X21501474
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