Structure and substructure connectivity of balanced hypercubes

08/06/2018

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by   Huazhong Lü, et al.

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The connectivity of a network directly signifies its reliability and fault-tolerance. Structure and substructure connectivity are two novel generalizations of the connectivity. Let H be a subgraph of a connected graph G. The structure connectivity (resp. substructure connectivity) of G, denoted by κ(G;H) (resp. κ^s(G;H)), is defined to be the minimum cardinality of a set F of connected subgraphs in G, if exists, whose removal disconnects G and each element of F is isomorphic to H (resp. a subgraph of H). In this paper, we shall establish both κ(BH_n;H) and κ^s(BH_n;H) of the balanced hypercube BH_n for H∈{K_1,K_1,1,K_1,2,K_1,3,C_4}.