Connectivity is an important parameter to measure fault-tolerance of networks. As a generalization, structure connectivity and substructure connectivity of networks were proposed. For connected graphs G and H, the H-structure connectivity κ(G;H) (resp. H-substructure connectivity κ~s(G;H)) of G is the minimum cardinality of a set of subgraphs F of G that each is isomorphic to H (resp. a connected subgraph of H) such that G - F is disconnected or the singleton, n-dimensional folded cross cube, FCQ_n, is a network obtained by adding edges to n-dimensional cross cubes. In this paper, we study star, path, and cycle structure connectivity and substructure connectivity of FCQ_n, where n > 8. For star (K_(1,m)) structure, we get that κ(FCQ_n;K_(1,m)) = κ~s(FCQ_n;K_(1,m)) =「(n+1)/2」 for 2 ≤ m ≤ n/2- For path (P_k) structure, we show that for 3 ≤ k ≤ n + 1, if k is odd, then κ(FCQ_n;P_k) = κ~s(FCQ_n;P_k) = 「(2(n+1))/(k+1)」, if k is even, then κ(FCQ_n;P_k) = κ~s(FCQ_n;P_k) = 「(2(n+1))/k」. For cycle (C_k) structure, we prove that κ(FCQ_n;C_k) = κ~s(FCQ_n;P_k). Further, we calculate κ(FCQ_n; C_(2k-1)) = 「(n+1)/(k-1)」 for 4 ≤ k ≤ n + 2 and C_(2k)-structure connectivity of FCQ_n is 「(n+1)/k」 +1 for 6≤k<n + l and even k.
Lina Ba、Heping Zhang
展开 >
School of Finance and Mathematics, Huainan Normal University, Huainan, Anhui 232038, China
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China
NETL
NSTL
Oxford Univ Press
