The Structure Fault Tolerance Of Arrangement Graphs

The arrangement graph A(n,k) is a prominent underlying topology for multi-processor/multicomputer networks. In this paper, we study the structure fault tolerance of A(n,k) for two structures of interest and significance - the m-leaves star S-m, and the m-leaves 2-step star T-2m. Let G be a connected graph and H a connected subgraph of G. The H-structure connectivity k (G; H) (resp. H-substructure connectivity k(s)(G; H)) of G is the cardinality of a minimum collection F = {H-1, H-2, ..., H-t}, such that for each and every 1 <= i <= t, H-i subset of G and H-i is isomorphic to H (resp. isomorphic to a connected subgraph of H), and the removal of F disconnects G. In this paper, we will determine k (A(n,k) ; H) and k(s) (A(n,k); H) for H is an element of {S-m,T-2m}. Our result adds to the many known, desirable properties of A(n,k), providing more perspectives when considering its candidacy as an interconnection network for multiprocessor systems. (C) 2021 Elsevier Inc. All rights reserved.