A complete classification of which $(n,k)$-star graphs are Cayley graphs

Abstract

The $(n,k)$-star graphs are an important class of interconnection networks that generalize star graphs, which are superior to hypercubes. In this paper, we continue the work begun by Cheng et al.~(Graphs and Combinatorics 2017) and complete the classification of all the $(n,k)$-star graphs that are Cayley.

We have proved the conjecture in the first version, thus completed the classification of which $(n,k)$-star graphs are Cayley