International Journal of Foundations of Computer Science ( IF 0.523 ) Pub Date : 2021-01-25 , DOI: 10.1142/s0129054121500076
Litao Guo; Mingzu Zhang; Shaohui Zhai; Liqiong Xu

Reliability of interconnection networks is important to design multiprocessor systems. The extra edge connectivity and component edge connectivity are two parameters for the reliability evaluation. The $k$-extra edge connectivity $λk(G)$ is the cardinality of the minimum extra edge cut $F$ such that $G−F$ is not connected and each component of $G−F$ has at least $k$ vertices. The $t$-component edge connectivity $λt(G)$ of a graph $G=(V,E)$ is the minimum edge number of a set $F$ such that $G−F$ is not connected and $G−F$ has at least $t$ components. In this paper, we find the relation of extra edge connectivity and component edge connectivity for regular networks. As an application, we determine the component edge connectivity of BC networks, $k$-ary $n$-cubes, enhanced hypercubes.

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