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Discussiones Mathematicae Graph Theory 25(3) (2005) 427-433
DOI: https://doi.org/10.7151/dmgt.1294

ON A SPHERE OF INFLUENCE GRAPH IN A ONE-DIMENSIONAL SPACE

Zbigniew Palka and Monika Sperling

Department of Algorithmics and Programming
Adam Mickiewicz University
Umultowska 87, 61-614 Poznań, Poland
e-mail: palka@amu.edu.pl
e-mail: dwight@amu.edu.pl

Abstract

A sphere of influence graph generated by a finite population of generated points on the real line by a Poisson process is considered. We determine the expected number and variance of societies formed by population of n points in a one-dimensional space.

Keywords: cluster, sphere of influence graph.

2000 Mathematics Subject Classification: Primary 60D05;
Secondary 60C05, 05C80.

References

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Received 9 September 2004
Revised 4 May 2005