Abstract For d> 0, define G (Q 3, d) to be the graph whose set of vertices is the rational space
Q 3, where two vertices are adjacent if and only if they are a Euclidean distance d apart. Let …

Abstract For S⊆ R, positive integer n, and d> 0, let G (S n, d) be the graph whose vertex set
is S n where any two vertices are adjacent if and only if they are Euclidean distance d apart …

For $ d> 0$, define $ G (\mathbb {Q}^ 3, d) $ to be the graph whose set of vertices is the
rational space $\mathbb {Q}^ 3$, where two vertices are adjacent if and only if they are a …

For any positive definite rational quadratic form q of n variables let G (ℚ n, q) denote the
graph with vertices ℚ n and x, y∈ ℚ n connected if and only if q (x− y)= 1. This notion …

For $ S\subseteq\mathbb {R} $, positive integer $ n $, and $ d> 0$, let $ G (S^ n, d) $ be the
graph whose vertex set is $ S^ n $ where any two vertices are adjacent if and only if they are …

For d > 0, designate by G (Q³, d) the graph whose set of vertices is the rational space Q³,
with any two vertices being adjacent if and only if they are Euclidean distance d apart. Deem …