On d-Unit Graphs in Rn

Abstract

In this paper, the unit dimension of a graph with respect to a metric d on the space Rn is defined. This generalizes the concept of
the Euclidean unit dimension of a graph in the space Rn as defined by various authors in [1], [2], [3], and [4]. It is also shown that two
equivalent metrics in Rn may yield different unit dimensions of some complete graphs.