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}
}