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Many multiprocessor systems have interconnection networks as underlyingtopologies and an interconnection network is usually represented by a graphwhere nodes represent processors and links represent communication linksbetween processors. In 2016, Zhang et al. proposed the $g$-extra diagnosabilityof $G$, which restrains that every component of $G-S$ has at least $(g +1)$vertices. As an important variant of the hypercube, the $n$-dimensional crossedcube $CQ_{n}$ 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-extradiagnosability of $CQ_{n}$ is $4n-6$ under the PMC model $(n\geq5)$ and MM$^*$model $(n\geq7)$.

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