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Neighbor connectivity of hypercube-based compound network.

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Title: Neighbor connectivity of hypercube-based compound network.
Authors: Li, Yifan1 (AUTHOR) llyfliyifan@163.com, Zhou, Shuming1,2,3 (AUTHOR) zhoushuming@fjnu.edu.cn, Zhang, Qifan1 (AUTHOR) zqf_1995@163.com
Source: Discrete Applied Mathematics. May2026, Vol. 384, p1-15. 15p.
Subjects: Hypercube networks (Computer networks), Graph connectivity, Computer networks, Computer network reliability
Abstract: For a network G , the subversion at the vertex set (resp., edge set) of G is defined as the removal of the closed neighborhood of the vertex set (resp., all end vertices of the edge set) from G , where the vertex set (resp., edge set) is referred as subverted vertices (resp., edges). Neighbor connectivity and edge neighbor connectivity serve as key indicators for assessing the subversion of spy networks and network disruptions throughout the deletion of closed neighborhood. The neighbor connectivity κ N B (G) (resp., edge neighbor connectivity λ N B (G)) of a network G is defined as the minimum number of subverted vertices (resp., edges) required to disconnect it, make it empty or complete (resp., trivial). Gu et al. (IEEE Trans. Netw. Sci. Eng. 11 (5) (2024) 1-13) conjectured that whether κ NB (G) = δ (G) − 1 2 + 1 holds for all compound graphs G constructed by the underlying block Q n. In this paper, we solve this conjecture and determine the (edge) neighbor connectivity of a class of hypercube-based compound network, including half hypercube, hierarchical hypercube, hierarchical cubic network and dual-cube-like network. In addition, we present network vulnerability analysis algorithms based on neighborhood fault pattern. To evaluate their effectiveness, taking the half hypercube, hierarchical cubic network and real-world network dwt-918 as examples, we perform experimental simulations to analyze both the cardinality distribution of subverted vertices and topological configurations of survival graph. [ABSTRACT FROM AUTHOR]
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Abstract:For a network G , the subversion at the vertex set (resp., edge set) of G is defined as the removal of the closed neighborhood of the vertex set (resp., all end vertices of the edge set) from G , where the vertex set (resp., edge set) is referred as subverted vertices (resp., edges). Neighbor connectivity and edge neighbor connectivity serve as key indicators for assessing the subversion of spy networks and network disruptions throughout the deletion of closed neighborhood. The neighbor connectivity κ N B (G) (resp., edge neighbor connectivity λ N B (G)) of a network G is defined as the minimum number of subverted vertices (resp., edges) required to disconnect it, make it empty or complete (resp., trivial). Gu et al. (IEEE Trans. Netw. Sci. Eng. 11 (5) (2024) 1-13) conjectured that whether κ NB (G) = δ (G) − 1 2 + 1 holds for all compound graphs G constructed by the underlying block Q n. In this paper, we solve this conjecture and determine the (edge) neighbor connectivity of a class of hypercube-based compound network, including half hypercube, hierarchical hypercube, hierarchical cubic network and dual-cube-like network. In addition, we present network vulnerability analysis algorithms based on neighborhood fault pattern. To evaluate their effectiveness, taking the half hypercube, hierarchical cubic network and real-world network dwt-918 as examples, we perform experimental simulations to analyze both the cardinality distribution of subverted vertices and topological configurations of survival graph. [ABSTRACT FROM AUTHOR]
ISSN:0166218X
DOI:10.1016/j.dam.2025.12.049