1-Extra 3-component edge connectivity of modified bubble-sort networks

Abstract Edge connectivity can measure the reliability of a network. Extra edge connectivity and component edge connectivity are the generalization of the classical edge connectivity. The extra component edge connectivity is the combination of the extra edge connectivity and component edge connectivity which can be used to measure the reliability of a network more precisely. The modified bubble-sort graph $MB_n$ is one of the important interconnection network topologies. In this paper, we study the 1-extra 3-component edge connectivity $c\lambda_3^1 (MB_n )$ of the modified bubble-sort graph and prove that $c\lambda_3^1 (MB_n )=4n-6$.