Distance graphs in vector spaces over finite fields, coloring and pseudo-randomness

Hart, Derrick; Iosevich, Alex; Koh, Doowon; Senger, Steve; Uriarte-Tuero, Ignacio

Distance graphs in vector spaces over finite fields, coloring and pseudo-randomness

Authors

Uriarte-Tuero, Ignacio

Description

In this paper we systematically study various properties of the distance graph in ${\Bbb F}_q^d$, the $d$-dimensional vector space over the finite field ${\Bbb F}_q$ with $q$ elements. In the process we compute the diameter of distance graphs and show that sufficiently large subsets of $d$-dimensional vector spaces over finite fields contain every possible finite configurations.