Structure connectivity and substructure connectivity of twisted hypercubes [article]

Dong Li, Xiaolan Hu, Huiqing Liu
2018 arXiv   pre-print
Let G be a graph and T a certain connected subgraph of G. The T-structure connectivity κ(G; T) (or resp., T-substructure connectivity κ^s(G; T)) of G is the minimum number of a set of subgraphs F={T_1, T_2, ..., T_m} (or resp., F={T^'_1, T^'_2, ..., T^'_m}) such that T_i is isomorphic to T (or resp., T^'_i is a connected subgraph of T) for every 1≤ i ≤ m, and F's removal will disconnect G. The twisted hypercube H_n is a new variant of hypercubes with asymptotically optimal diameter introduced
more » ... X.D. Zhu. In this paper, we will determine both κ(H_n; T) and κ^s(H_n; T) for T∈{K_1,r, P_k}, respectively, where 3≤ r≤ 4 and 1 ≤ k ≤ n.
arXiv:1803.08408v1 fatcat:c7ztxi555nfxvix6r5hapearim