For any positive definite rational quadratic form
q of
n variables let
G(Qn,q) denote the graph
with vertices
Qn
and
x,y∈Qn connected
if and only if
q(x−y)=1.
This notion generalises standard Euclidean distance graphs. In this article we study
these graphs and show how to find the exact value of clique number of the
G(Qn,q).
We also prove rational analogue of the Beckman–Quarles theorem that any unit-preserving
bijection of Qn
onto itself is an isometry.
