Some colouring problems for unit-quadrance graphs

Abstract

The quadrance between two points $A_1=(x_1,y_1)$ and $A_2=(x_2,y_2)$ is the number $Q(A_1,A_2)=(x_1-x_2{)}^2+(y_1-y_2{)}^2$. Let $q$ be an odd prime power and $F_q$ be the finite field with $q$ elements. The unit-quadrance graph $D_q$ has the vertex set $F_q^2$, and $X,Y\in F_q^2$ are adjacent if and only if $Q(A_1,A_2)=1$. In this paper, we study some colouring problems for the unit-quadrance graph $D_q$ and discuss some open problems.

Cited by in corpus (1)

• Integral point sets over finite fields