Connectivity and Fault-Tolerance in Random Regular Graphs

Keywords and Synonyms

Robustness      

Problem Definition

A new model of random graphs was introduced in [7], that of random regular graphs with edge faults (denoted hereafter by ${ G_{n,p}^{r} }$), obtained by selecting the edges of a random member of the set of all regular graphs of degree r independently and with probability p. Such graphs can represent a communication network in which the links fail independently and with probability ${ f=1-p }$. A formal definition of the probability space ${ G_{n,p}^{r} }$ follows.

Definition 1 (the G ^r _n, p probability space)

Let ${ G_{n}^{r} }$ be the probability space of all random regular graphs with n vertices where the degree of each vertex is r. The probability space ${ G_{n,p}^{r} }$ of random regular graphs with edge faults is constructed by the following two subsequent random experiments: first, a random regular graph is chosen from the space ${ G_{n}^{r} }$and, second, each edge is randomly and independently deleted...