Conditional fault tolerance of arrangement graphs

Abstract

Fault tolerance is especially important for interconnection networks, since the growing size of the networks increases its vulnerability to component failures. A classic measure for the fault tolerance of a network in the case of vertex failures is its connectivity. Given a network based on a graph G and a positive integer h, the R h -connectivity of G is the minimum cardinality of a set of vertices in G, if any, whose deletion disconnects G, and every remaining component has minimum degree at least h. This paper investigates the R h -connectivity of the ( n , k ) -arrangement graph A n , k for h = 1 and h = 2 , and determines that κ 1 ( A n , k ) = ( 2 k − 1 ) ( n − k ) − 1 and κ 2 ( A n , k ) = ( 3 k − 2 ) ( n − k ) − 2 , respectively.