Abstract
A planar point set X is called a k-distance set if there are exactly k distinct distances defined by every two points in X,and the longest distance is called diameter D. The set of the endpoints of all diameters is denoted by XD. Let m = m( X) = | XD| be the number of elements of XD,and the diameter graph DG( XD) be all diameters in X. There are many results on determining the value of g( k) when k≤6,where g( k) is the number of points of the largest point set having k distinct distances. We consider planar point sets for the case of k≥7. Firstly,we perform an analysis on the degree value d( v) of all vertices in k-distance DG( XD) for m = | XD| = 2k-1,and obtain that d( v) ≤2. Based on this result,we research the case of 7-distance. We get XD= R15-3 when the 7-distance sets DG( XD) = P10∪P2. The result provides a theoretical foundation for further discussions on 7-distance sets.
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.
