Geodesic
The generalized 4-connectivity of balanced hypercubes
Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 3, pp. 1079-1106

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The balanced hypercube is a kind of highly symmetrical network and possesses many good properties. Generalized connectivity is a new measurement of interconnection networks' fault tolerance. The internally disjoint N-trees are edge-disjoint trees but with intersecting vertex set N. Let κ(N) be the maximum number of internally disjoint N-trees and the generalized k-connectivity of G be κ_k(G)=min{κ(N) | N ⊂ V(G) and | N | =k}. In this paper, we study the n-dimensional balanced hypercube BH_n and demonstrate that κ_4(BH_n)=2n-1 for n ≥ 1.
Keywords: interconnection network, balanced hypercube, generalized connectivity, fault tolerance 
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Cheng, Dongqin. The generalized 4-connectivity of balanced hypercubes. Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 3, pp. 1079-1106. http://geodesic.mathdoc.fr/item/DMGT_2024_44_3_a14/