On the 3-Extra Connectivity of Enhanced Hypercubes

Abstract

Reliability evaluation of interconnection networks is of significant importance to the design and maintenance of interconnection networks. The extra connectivity is an important parameter for the reliability evaluation of interconnection networks. Given a graph [Formula: see text] and a positive integer [Formula: see text], the [Formula: see text]-extra connectivity, denoted by [Formula: see text], is the minimum cardinality of a set of vertices in [Formula: see text], if exists, whose deletion disconnects [Formula: see text] and leaves each remaining component with at least [Formula: see text] vertices. In this paper, we show that the 3-extra connectivity of the [Formula: see text]-enhanced hypercube is [Formula: see text] for [Formula: see text] and [Formula: see text]. Some previous results in [IEEE Trans. Comput. 63 (2014) 1594–1600] and [Theor. Comput. Sci. 799 (2019) 22–31] are extended.