Component connectivity of augmented cubes

Zhang, Qifan; Zhou, Shuming; Cheng, Eddie

doi:10.1016/j.tcs.2023.113784

Cited by 5 publications

(1 citation statement)

References 35 publications

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“…Zhao and Yang studied the n-dimensional folded hypercube FQ n for 1 ≤ m ≤ n − 1 and n ≥ 8 [17]. Zhang et al [18] determined the (m + 1)-component connectivity of augmented cubes. In addition, the m-component connectivity (m = 3, m = 4) has been studied for many graphs: alternating group networks AN n [19,20], split-star networks [20], hierarchical star networks [21], balanced hypercube [22], bubble-sort star graphs, and burnt pancake graphs [23].…”

Section: Introductionmentioning

confidence: 99%

The m-Component Connectivity of Leaf-Sort Graphs

Wang,

Li,

Zhao

2024

Mathematics

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Connectivity plays an important role in measuring the fault tolerance of interconnection networks. As a special class of connectivity, m-component connectivity is a natural generalization of the traditional connectivity of graphs defined in terms of the minimum vertex cut. Moreover, it is a more advanced metric to assess the fault tolerance of a graph G. Let G=(V(G),E(G)) be a non-complete graph. A subset F(F⊆V(G)) is called an m-component cut of G, if G−F is disconnected and has at least m components (m≥2). The m-component connectivity of G, denoted by cκm(G), is the cardinality of the minimum m-component cut. Let CFn denote the n-dimensional leaf-sort graph. Since many structures do not exist in leaf-sort graphs, many of their properties have not been studied. In this paper, we show that cκ3(CFn)=3n−6 (n is odd) and cκ3(CFn)=3n−7 (n is even) for n≥3; cκ4(CFn)=9n−212 (n is odd) and cκ4(CFn)=9n−242 (n is even) for n≥4.

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