Structure and substructure connectivity of balanced hypercubes

2018/08/06 by Lü, Huazhong, Wu, Tingzeng
#05C40 #68R10 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.02375

Abstract

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∈\K₁,K_1,1,K_1,2,K_1,3,C₄\.

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