EDGE-WIENER INDEX OF LEVEL-3 SIERPINSKI SKELETON NETWORK

Fractals Pub Date : 2024-05-14 DOI:10.1142/s0218348x24500816
CAIMIN DU, YIQI YAO, LIFENG XI
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Abstract

The edge-Wiener index is an important topological index in Chemical Graph Theory, defined as the sum of distances among all pairs of edges. Fractal structures have received much attention from scientists because of their philosophical and aesthetic significance, and chemists have even attempted to synthesize various types of molecular fractal structures. The level-3 Sierpinski triangle is constructed similarly to the Sierpinski triangle and its skeleton networks have self-similarity. In this paper, by using the method of finite pattern, we obtain the edge-Wiener index of skeleton networks according to level-3 Sierpinski triangle. This provides insights for a better understanding of molecular fractal structures.

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第三级西尔平斯基骨架网络的边-维纳指数
边-维纳指数是化学图论中的一个重要拓扑指数,定义为所有边对之间的距离之和。分形结构因其哲学和美学意义而备受科学家关注,化学家甚至尝试合成各种类型的分子分形结构。三级西尔平斯基三角形的构造与西尔平斯基三角形类似,其骨架网络具有自相似性。本文利用有限模式的方法,根据第 3 层 Sierpinski 三角形得到了骨架网络的边缘-维纳指数。这为更好地理解分子分形结构提供了启示。
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