ECCENTRIC DISTANCE SUM OF SUBSTITUTION TREE NETWORKS

Jinmyong Kim and Myongjin Kim
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Jinmyong Kim: Faculty of Mathematics, Kim Il Sung University, Pyongyang, DPR Korea
Myongjin Kim: ��Pyongyang Software Joint Development Corporation, Pyongyang, DPR Korea

FRACTALS (fractals), 2021, vol. 29, issue 06, 1-13

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.

Keywords: Substitution Network; Fractal Network; Average Geodesic Distance; Eccentric Distance Sum; Self-similar Measure (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21501474

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