Abstract The connectivity is an important indicator to evaluate the robustness of a network. Many works have focused on connectivity-based reliability analysis for decades. As a generalization of connectivity, H-structure connectivity and H-substructure connectivity were proposed to evaluate the robustness of networks. In this paper, we investigate the H-structure connectivity and H-substructure connectivity of alternating group graph AGn when H is isomorphic to K1,t, Pl and Ck, which are generalizations of the previous results for H ∈ {K1, K1,1, K1,2}. And we show that κ ( A G n ; K 1 , t ) = κ s ( A G n ; K 1 , t ) = n − 2 ( 1 ≤ t ≤ 2 n − 6 ) , κ ( A G n ; P l ) = κ s ( A G n ; P l ) = ⌈ 2 n − 4 l − ⌊ l / 3 ⌋ ⌉ ( 1 ≤ l ≤ 3 n − 7 ), κ ( A G n ; C k ) = ⌈ n − 2 ⌊ k / 3 ⌋ ⌉ and κ s ( A G n ; C k ) = ⌈ 2 n − 4 k − ⌊ k / 3 ⌋ ⌉ ( 6 ≤ k ≤ 3 n − 6 ).

中文翻译：

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交替群图的结构和子结构连通性

摘要 连通性是评价网络健壮性的重要指标。几十年来，许多工作都集中在基于连通性的可靠性分析上。作为连通性的概括，提出了 H 结构连通性和 H 子结构连通性来评估网络的鲁棒性。在本文中，我们研究了当 H 与 K1,t, Pl 和 Ck 同构时交替群图 AGn 的 H-结构连通性和 H-子结构连通性，这是对 H ∈ {K1, K1,1 的先前结果的推广, K1,2}。我们证明κ (AG n ; K 1 , t ) = κ s ( AG n ; K 1 , t ) = n − 2 ( 1 ≤ t ≤ 2 n − 6 ) , κ (AG n ; P l ) = κ s ( AG n ; P l ) = ⌈ 2 n − 4 l − ⌊ l / 3 ⌋ ⌉ ( 1 ≤ l ≤ 3 n − 7 ), κ ( AG n ; C k ) = ⌈ n − 2 ⌊ k / 3 ⌋ ⌉ 和 κ s ( AG n ; C k ) = ⌈ 2 n − 4 k − ⌊ k / 3 ⌋ ⌉ ( 6 ≤ k ≤ 3 n − 6 )。