Edge-Wiener Index of Level-3 Sierpinski Skeleton Network

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.