λ′λ′-optimally connected mixed Cayley graphs

A restricted edge cut of a graph XX is an edge set whose removal disconnects XX into non-trivial components. The cardinality of the minimum restricted edge cut is the restricted edge connectivity, denoted by λ′(X)λ′(X). If XX has restricted edge cuts and λ′(X)λ′(X) achieves the upper bound of the restricted edge connectivity, XX is said to be λ′λ′-optimal. In this work, we will prove that for all but a few exceptions, the mixed Cayley graph is λ′λ′-optimal.