✍ Scribed by Victor Chepoi; Sandi Klavẑar
No coin nor oath required. For personal study only.
In this note we present some new results on distances in benzenoids. An algorithm is presented which, for a given benzenoid system G bounded by a simple circuit 2 with n vertices, computes the Wiener index of G in O(n) time. Also we show that benzenoid systems have a convenient dismantling scheme, which can be derived by applying breadth-first search to their dual graphs. Our last result deals with the clustering problem of sets of atoms of benzenoids systems. We show how the k-means clustering algorithm (for points in Euclidean space) can be efficiently
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