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

TL;DR

This paper investigates the robustness and diagnosability of crossed cubes, a type of interconnection network, establishing new bounds on their super 3-extra connectivity and diagnosability under specific models.

Contribution

It proves that crossed cubes are tightly (4n-9) super 3-extra connected for n≥7 and determines their 3-extra diagnosability as 4n-6 under the PMC and MM* models.

Findings

Crossed cubes are tightly (4n-9) super 3-extra connected for n≥7.

The 3-extra diagnosability of crossed cubes is 4n-6.

Results improve understanding of fault tolerance in interconnection networks.

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 $(n\geq7)$.