English

On the independence number of regular graphs of matrix rings

Combinatorics 2024-05-15 v1

Abstract

Consider a graph on the non-singular matrices over a finite field, in which two distinct non-singular matrices are joined by an edge whenever their sum is singular. We prove an upper bound for the independence number of this graph. As a consequence, we obtain a lower bound for its chromatic number that significantly improves a previous result of Tomon.

Keywords

Cite

@article{arxiv.2405.08734,
  title  = {On the independence number of regular graphs of matrix rings},
  author = {Bogdan Nica},
  journal= {arXiv preprint arXiv:2405.08734},
  year   = {2024}
}