Abstract
A β-skeleton, β⩾1, 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 β determines the size and shape of the lune-based neighbourhood. A β-skeleton of a random planar set is usually a disconnected graph for β>2. With the increase of β, the number of edges in the β-skeleton of a random graph decreases. We show how to grow stable β-skeletons, which are connected for any given value of β and characterise morphological transformations of the skeletons governed by β and a degree of approximation. We speculate how the results obtained can be applied in biology and chemistry.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
