# Maximum Independent Sets Partition of (n,k)-Star Graphs

## TL;DR

This paper establishes the maximum independent sets partition of (n,k)-star graphs, enabling the precise calculation of their independent and chromatic numbers, which were previously unknown or incorrectly proven.

## Contribution

It generalizes prior results and provides the correct maximum independent sets partition for (n,k)-star graphs, resolving previous inaccuracies.

## Key findings

- Exact values of independent number and chromatic number derived
- Maximum independent sets partition explicitly constructed
- Corrected previous incorrect proof

## Abstract

The (n,k)-star graph is a very important computer modelling. The independent number and chromatic number of a graph are two important parameters in graph theory. However, we did not know the values of this two parameters of the (n,k)-star graph since it was proposed. In [18], Wei et. al. declared that they determined the independent number of the (n,k)-star graph, unfortunately their proof is wrong. This paper generalize their result and present a maximum independent sets partition of (n,k)-star graph. From that we can immediately deduce the exact value of the independent number and chromatic number of (n,k)-star graph.