Structure Fault-tolerance of Arrangement Graphs

Given a connected graph G and a connected subgraph H of G . The H-structure connectivity kappa(G ; H ) of G is the minimal cardinality of a set of subgraphs F = {J(1) , J(2) , . . . , J(m) } in G , where J(i)congruent to H (1 <= i <= m ), and the deletion of F disconnects G . Similarly, the H-substructure connectivity kappa(s) (G ; H ) of G is the minimal cardinality of a set of subgraphs F = {J(1) , . . . , J(m) } in G , where J(i) (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 kappa(A(n,k) ; H ) and kappa(s) (A(n,k) ; H ) of the (n, k )-arrangement graph A(n,k) , where H is an element of{K-1,(m1), P-m2} (m(1)>= 1 , m(2)>= 4 ). (C) 2020 Elsevier Inc. All rights reserved.