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WROCŁAW UNIVERSITY
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TECHNOLOGY

Contents of PMS, Vol. 20, Fasc. 2,
pages 391 - 397
 

VERTICES OF DEGREE ONE IN A RANDOM SPHERE OF INFLUENCE GRAPH

Monika Sperling

Abstract: The sphere of influence graph of the set of vertices in Rd is constructed by identifying the nearest neighbour of each vertex, centering a ball at each vertex so that its nearest neighbour lies on the boundary, and joining two vertices by an edge if and only if their balls intersect. We determine the expectation and variance of the number of vertices of degree one in the random sphere of influence graph.

1991 AMS Mathematics Subject Classification: Primary -; Secondary -;

Key words and phrases: -

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