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arXiv · 2611.00764

Edge-structure fault diameters of exchanged hypercubes

Lihui Dong·Zhuo Li
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Abstract

We determine the edge-structure and edge-substructure fault diameters of the exchanged hypercube $EH(s,t)$ for every $1\le s\le t$. Both parameters equal $s+t+4$, two more than the fault-free diameter, except for $EH(2,2)$, where both are nine, and $EH(1,1)$, where they are five and six, respectively. This holds even though an admissible family may remove up to $2s$ vertices, more than the vertex connectivity $s+1$. For every $s\ge2$, the maximum is attained by $s$ parallel fault edges in class $0$. For $s\ge3$, the structure-fault diameter exceeds the classical $s$-vertex-fault diameter by exactly one.

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Lihui Dong, Zhuo Li. 2026-10-31. Edge-structure fault diameters of exchanged hypercubes. https://arxiv.org/abs/2611.00764

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