Structure and substructure connectivity of alternating group graphs

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(AGn;K1,t)=κs(AGn;K1,t)=n−2 (1≤t≤2n−6),κ(AGn;Pl)=κs(AGn;Pl)=⌈2n−4l−⌊l/3⌋⌉ (1≤l≤3n−7), κ(AGn;Ck)=⌈n−2⌊k/3⌋⌉ and κs(AGn;Ck)=⌈2n−4k−⌊k/3⌋⌉ (6≤k≤3n−6).