AbstractLet G be the graph obtained from all the rational points in the d-space Ed by connecting every pair at Euclidean distance one. It is known that G is a connected graph, provided d ⩾ 5.We establish an inequality of the form distG(x, y) ⩽ ⌈|x − y|⌉ + 1, for all d ⩾ 8, between the Euclidean distance |x − y| of any two rational points x and y and their corresponding distance distG(x, y) in the graph G. A slightly weaker relation is shown to hold in dimensions 5, 6 and 7
An ϵ-distance-uniform graph is one with a critical distance d such that from every vertex, all but a...
AbstractIn this note, inequalities between the distance degrees of distance degree regular graphs an...
The doctoral thesis describes problems concerning graphs that can be represented in the Euclidean pl...
AbstractLet G be the graph obtained from all the rational points in the d-space Ed by connecting eve...
A faithful (unit) distance graph in Rd is a graph whose set of vertices is a finite sub-set of the d...
AbstractIt is proved that a number d>0 can appear as the Euclidean distance between two vertices in ...
Abstract. For a number eld K R, consider the graph G(Kd), whose vertices are elements of Kd, with a...
AbstractFos S ⊆ R, let G(Sd) denote the graph, obtained from all the points of the real d-space Rd h...
AbstractLet Un be the infinite graph with n-dimensional rational space Qn as vertex set and two vert...
The unit distance graph G1Rd is the infinite graph whose nodes are points in Rd, with an edge betwee...
AbstractA unit-distance graph in Rn is a graph with a subset of Rn as the vertex set and two vertice...
AbstractLet G=(V,E) be a digraph with diameter D≠1. For a given integer 1⩽t⩽D, the t-distance connec...
Let be a distance regular graph with diameter d and valency k. For nonnegative integers i and j, wit...
AbstractA graph G=(V,E) is called a unit-distance graph in the plane if there is an embedding of V i...
A distance graph G(X;D) is a graph whose set of vertices is the set of points X of a metric space (X...
An ϵ-distance-uniform graph is one with a critical distance d such that from every vertex, all but a...
AbstractIn this note, inequalities between the distance degrees of distance degree regular graphs an...
The doctoral thesis describes problems concerning graphs that can be represented in the Euclidean pl...
AbstractLet G be the graph obtained from all the rational points in the d-space Ed by connecting eve...
A faithful (unit) distance graph in Rd is a graph whose set of vertices is a finite sub-set of the d...
AbstractIt is proved that a number d>0 can appear as the Euclidean distance between two vertices in ...
Abstract. For a number eld K R, consider the graph G(Kd), whose vertices are elements of Kd, with a...
AbstractFos S ⊆ R, let G(Sd) denote the graph, obtained from all the points of the real d-space Rd h...
AbstractLet Un be the infinite graph with n-dimensional rational space Qn as vertex set and two vert...
The unit distance graph G1Rd is the infinite graph whose nodes are points in Rd, with an edge betwee...
AbstractA unit-distance graph in Rn is a graph with a subset of Rn as the vertex set and two vertice...
AbstractLet G=(V,E) be a digraph with diameter D≠1. For a given integer 1⩽t⩽D, the t-distance connec...
Let be a distance regular graph with diameter d and valency k. For nonnegative integers i and j, wit...
AbstractA graph G=(V,E) is called a unit-distance graph in the plane if there is an embedding of V i...
A distance graph G(X;D) is a graph whose set of vertices is the set of points X of a metric space (X...
An ϵ-distance-uniform graph is one with a critical distance d such that from every vertex, all but a...
AbstractIn this note, inequalities between the distance degrees of distance degree regular graphs an...
The doctoral thesis describes problems concerning graphs that can be represented in the Euclidean pl...
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