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

## TL;DR

This paper fully classifies which $(n,k)$-star graphs are Cayley graphs, extending previous work and providing a comprehensive understanding of their algebraic structure.

## Contribution

It completes the classification of Cayley $(n,k)$-star graphs, advancing the algebraic understanding of these important interconnection networks.

## Key findings

- Identifies all $(n,k)$-star graphs that are Cayley graphs
- Provides a complete characterization of Cayley $(n,k)$-star graphs
- Extends previous partial classifications

## 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.