The Maximum Vertex Degree of a Graph on Uniform Points in [0, 1]d

摘要: This article continues an investigation begun in [2]. A random graph G n ( x ) is constructed on independent points U 1 , · ··, distributed uniformly [0, 1] d ≧ 1, which two distinct such are joined by edge if the l ∞ -distance between them at most some prescribed value 0 Almost-sure asymptotic results obtained for convergence/divergence of minimum vertex degree graph, as number becomes large and distance allowed to vary with n. The largest nearest neighbor link smallest that has no vertices zero, shown satisfy Series sequence criteria distances {x } provided guarantee be complete, a.s. These imply limiting behavior diameter set.