VERTICES OF DEGREE ONE IN A RANDOM SPHERE OF INFLUENCE
GRAPH
Abstract: The sphere of influence graph of the set of vertices in 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: -