Shiying Wang and Xiaolei Ma, The tightly super 2-extra connectivity and 2-extra diagnosability of crossed cubes, Volume 2018, Number 1, Pages 201-218, 2018

# Shiying Wang and Xiaolei Ma, The tightly super 2-extra connectivity and 2-extra diagnosability of crossed cubes, Volume 2018, Number 1, Pages 201-218, 2018

Abstract: Connectivity and diagnosability play an important role in measuring the fault tolerance of interconnection networks. As a topology structure of interconnection networks, the $n$-dimensional crossed cube $CQ_{n}$ has many good properties. In this paper, we study the 2-extra connectivity and 2-extra diagnosability of $CQ_{n}$. We prove that $CQ_{n}$ is tightly $(3n-5)$ super 2-extra connected for $n\geq 5$, and the 2-extra diagnosability of $CQ_{n}$ is $3n-3$ under the PMC model $(n\geq5)$ and MM* model $(n\geq6)$.

Keywords: Interconnection network; Connectivity; Diagnosability; Crossed cube.