THE EDGE-WIENER INDEX OF FRACTAL NETWORKS: A STUDY ON THE LEVEL-3 SIERPINSKI TRIANGLE

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The edge-Wiener index, as an edge-based variant of the Wiener index, serves as an important topological descriptor for characterizing network structures. In this paper, we study the skeleton network derived from the classic fractal — the level-3 Sierpinski triangle — and investigate the exact analytical expression of its edge-Wiener index. [Formula: see text]By introducing the finite patterns method (Wang et al.), the geometric relations between edge pairs are classified into four fundamental patterns, and corresponding distance recursion relations are established. Based on pattern classification and self-similar measures, we derive an exact formula for the edge-Wiener index with respect to the iteration order [Formula: see text].