On growing connected ¦Â-skeletons

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• 作者：Andrew Adamatzky ^{andrew.adamatzky@uwe.ac.uk}
• 关键词：Proximity graphs ; ¦Â-Skeletons ; Pattern formation ; Morphogenesis
• 刊名：Computational Geometry
• 出版年：2013
• 出版时间：August, 2013
• 年：2013
• 卷：46
• 期：6
• 页码：805-816
• 全文大小：1867 K

文摘

A ¦Â-skeleton, , is a planar proximity undirected graph of a Euclidean points set, where nodes are connected by an edge if their lune-based neighbourhood contains no other points of the given set. Parameter ¦Â determines the size and shape of the lune-based neighbourhood. A ¦Â-skeleton of a random planar set is usually a disconnected graph for . With the increase of ¦Â, the number of edges in the ¦Â-skeleton of a random graph decreases. We show how to grow stable ¦Â-skeletons, which are connected for any given value of ¦Â and characterise morphological transformations of the skeletons governed by ¦Â and a degree of approximation. We speculate how the results obtained can be applied in biology and chemistry.