Derrick Hart, Alex Iosevich, Doowon Koh, Steve Senger, Ignacio Uriarte-Tuero
Published 2008-04-18Version 1
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.
Long paths in the distance graph over large subsets of vector spaces over finite fields
Cycles of arbitrary length in distance graphs on $\mathbb{F}_q^d$
Characterizing $2$-Distance Graphs and Solving the Equations $T_2(X)=kP_2$ or $K_m \cup K_n$
![QR code for arXiv:0804.3036 [math.CO]](http://oss.arxitics.com/images/favicon.svg)