The 2-Extra Connectivity and Diagnosability of Expanded 6-Ary n-Cubes

Connectivity and diagnosability play an important role in measuring the fault tolerance of interconnection networks [Formula: see text]. A faulty set [Formula: see text] is called a [Formula: see text]-extra faulty set if every component of [Formula: see text] has more than [Formula: see text] vertices. A [Formula: see text]-extra cut of [Formula: see text] is a [Formula: see text]-extra faulty set [Formula: see text] such that [Formula: see text] is disconnected. The minimum cardinality of a [Formula: see text]-extra cut is said to be the [Formula: see text]-extra connectivity of [Formula: see text]. A new measure for fault diagnosis of [Formula: see text] restrains that every fault-free component has at least [Formula: see text] fault-free vertices, which is called the [Formula: see text]-extra diagnosability of [Formula: see text]. As a topology structure of interconnection networks, the expanded [Formula: see text]-ary [Formula: see text]-cube [Formula: see text] has many good properties. In this paper, we first prove that the 2-extra connectivity of [Formula: see text] is [Formula: see text], and then further determine that the 2-extra diagnosability of [Formula: see text] is [Formula: see text] under the PMC model for [Formula: see text] and under the MM[Formula: see text] model for [Formula: see text].