The distant graph of the projective line over a finite ring with unity

Edyta Bartnicka; Andrzej Matras

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arXiv · 1701.01263

The distant graph of the projective line over a finite ring with unity

Edyta Bartnicka·Andrzej Matras

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Abstract

We discuss the projective line $\mathbb{P}(R)$ over a finite associative ring with unity. $\mathbb{P}(R)$ is naturally endowed with the symmetric and anti-reflexive relation "distant". We study the graph of this relation on $\mathbb{P}(R)$ and classify up to isomorphism all distant graphs $G(R, \Delta)$ for rings $R$ up to order $p^5$, $p$ prime.

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Edyta Bartnicka, Andrzej Matras. 2017-01-05. The distant graph of the projective line over a finite ring with unity. https://arxiv.org/abs/1701.01263

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