Exact assessment of the super P_k -connectivity for the crossed cube interconnection network

A network is connected if there exists a path between any two distinct vertices. The vertex-connectivity of any connected network is the cardinality of its minimum vertex-cut. Then, a network is super connected if every of its minimum vertex-cuts always consists of a certain vertex’s neighborhood. Kung and Lin (Discret Appl Math 293: 143–156, 2021) recently defined the notion of the super cluster-connectivity as a novel, generalized measure to quantify a network’s connectedness level. This article is dedicated to establishing a deep analysis on the exact formula of super path-connectivity for the crossed cube interconnection network. Accordingly, a sufficient and necessary condition is presented to classify whether or not crossed cubes can be super path-connected.