The Distant Graph of the Projective Line Over a Finite Ring with Unity

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.