Applied Mathematics and Computation ( IF 3.472 ) Pub Date : 2020-09-14 , DOI: 10.1016/j.amc.2020.125639
Xiaowang Li; Shuming Zhou; Xiangyu Ren; Xia Guo

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 $\kappa \left(A{G}_{n};{K}_{1,t}\right)={\kappa }^{s}\left(A{G}_{n};{K}_{1,t}\right)=n-2$ ($1\le t\le 2n-6\right),$ $\kappa \left(A{G}_{n};{P}_{l}\right)={\kappa }^{s}\left(A{G}_{n};{P}_{l}\right)=⌈\frac{2n-4}{l-⌊l/3⌋}⌉$ ($1\le l\le 3n-7$), $\kappa \left(A{G}_{n};{C}_{k}\right)=⌈\frac{n-2}{⌊k/3⌋}⌉$ and ${\kappa }^{s}\left(A{G}_{n};{C}_{k}\right)=⌈\frac{2n-4}{k-⌊k/3⌋}⌉$ ($6\le k\le 3n-6$).

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