Structure Fault-tolerance of Arrangement Graphs

Abstract

Given a connected graph G and a connected subgraph H of G. The H-structure connectivity κ(G; H) of G is the minimal cardinality of a set of subgraphs F={J1,J2,…,Jm} in G, where Ji ≅H (1 ≤ i ≤ m), and the deletion of F disconnects G. Similarly, the H-substructure connectivity κs(G; H) of G is the minimal cardinality of a set of subgraphs F={J1,…,Jm} in G, where Ji (1 ≤ i ≤ m) is isomorphic to a connected subgraph of H, and the deletion of F disconnects G. Structure connectivity and substructure connectivity generalize the classical vertex-connectivity. In this thesis, we establish κ(An,k; H) and κs(An,k; H) of the (n, k)-arrangement graph An,k, where H∈{K1,m1,Pm2}(m1≥1,m2≥4).