On the g-extra connectivity of augmented cubes

A g-extra cut of a non-complete graph G, g > 0, is a set of vertices in G whose removal disconnects the graph, while every component in the survival graph contains at least g + 1 vertices. The g-extra connectivity of G then refers to the size of a minimum g-extra cut of G. The augmented hypercube, denoted by A Qn, n > 3, is a rich variant of the hypercube structure. In this paper, we present a sequence of construction based upper bounds of its g-extra connectivity, study its lower bound via the super connectedness property, and suggest an asymptotically tight bound. & COPY; 2023 Elsevier B.V. All rights reserved.