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arXiv · 2405.08734

On the independence number of regular graphs of matrix rings

Bogdan Nica
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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.

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Bogdan Nica. 2024-05-14. On the independence number of regular graphs of matrix rings. https://arxiv.org/abs/2405.08734

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