Focusing of Maximum Vertex Degrees in Random Faulty Scaled Sector Graphs

Abstract

In this paper we study the behavior of maximum out/in-degree of binomial/Poisson random scaled sector graphs in the presence of random vertex and edge faults. We prove that the probability distribution of maximum degrees for random faulty scaled sector graphs with $n$ vertices, where each vertex spans a sector of $\alpha$ radians, with radius $r_n\ll \sqrt{\ln n/n}$, become concentrated on two consecutive integers, under some natural assumptions of faulty probabilities.

14 pages, 1 figure

References in corpus (4)

• Monotone properties of random geometric graphs have sharp thresholds
• On the Degree Sequence of Random Geometric Digraphs
• The Distant-l Chromatic Number of Random Geometric Graphs
• Topological Properties of an Exponential Random Geometric Graph Process

Cited by in corpus (1)

• On the Degree Sequence of Random Geometric Digraphs