It is of great interest to analyze geodesics in fractals. We investigate the structure of geodesics in [Formula: see text]-dimensional Sierpinski gasket [Formula: see text] for [Formula: see text], and prove that there are at most eight geodesics between any pair of points in [Formula: see text]. Moreover, we obtain that there exists a unique geodesic for almost every pair of points in [Formula: see text].

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Let C be the middle-third Cantor set. Define C * C = {x * y : x, y ∈ C}, where * = +, −, •, ÷ (when * = ÷, we assume y = 0). Steinhaus [17] proved in 1917 that

The eigentime identity for random walks on networks is the expected time for a walker going from a node to another node. In this paper, our purpose is to calculate the eigentime identities of flower networks by using the characteristic polynomials of normalized Laplacian and recurrent structure of Markov spectrum.