Reliability of arrangement networks in terms of the h-restricted edge connectivity

The h -restricted edge connectivity lambda (h) is an important parameter to measure the reliability of massive parallel computing system. The lambda (h) of G is the minimum cardinality of a set of edges in G , if any, whose deletion disconnects G , and every remaining component has minimum degree at least h . The arrangement graph is a generalization of the star graph, but its order is more flexible than that of the star graph. This paper investigates the h -restricted edge connectivity of the ( n , k ) -arrangement graph A(n , k) , and determines that lambda (1 )( A(n , k)) = 2 k ( n - k ) - 2, lambda( 2) ( A (n , k) ) = 3 k ( n - k ) - 6 with k <= n - 2. (c) 2022 Elsevier Inc. All rights reserved.