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arXiv · 1708.01703

The tightly super 3-extra connectivity and 3-extra diagnosability of crossed cubes

Shiying Wang·Xiaolei Ma
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Abstract

Many multiprocessor systems have interconnection networks as underlying topologies and an interconnection network is usually represented by a graph where nodes represent processors and links represent communication links between processors. In 2016, Zhang et al. proposed the $g$-extra diagnosability of $G$, which restrains that every component of $G-S$ has at least $(g +1)$ vertices. As an important variant of the hypercube, the $n$-dimensional crossed cube $CQ_{n}$ has many good properties. In this paper, we prove that $CQ_{n}$ is tightly $(4n-9)$ super 3-extra connected for $n\geq 7$ and the 3-extra diagnosability of $CQ_{n}$ is $4n-6$ under the PMC model $(n\geq5)$ and MM$^*$ model $(n\geq7)$.

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Shiying Wang, Xiaolei Ma. 2017-08-05. The tightly super 3-extra connectivity and 3-extra diagnosability of crossed cubes. https://arxiv.org/abs/1708.01703

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