Focusing of Maximum Vertex Degrees in Random Faulty Scaled Sector Graphs

Details Focusing of Maximum Vertex Degrees in Random Faulty Scaled Sector Graphs Focusing of Maximum Vertex Degrees in Random Faulty Scaled Sector Graphs

2009-09-16

arxiv.org/abs/0909.2933v2

Mathematics

Combinatorics

14 pages, 1 figure

Scientific paper

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.

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