On the dimension of a graph

Our purpose in this note is to present a natural geometrical definition of the dimension of a graph and to explore some of its ramifications. In 1 we determine the dimension of some special graphs. We observe in 92 that several results in the literature are unified by the concept of the dimension of a graph, and state some related unsolved problems. We define the dimension of a graph G, denoted dim G, as the minimum number n such that G can be embedded into Euclidean n-space E, , with every edge of G having length 1. The vertices of C are mapped onto distinct points of E, , but there is no restriction on the crossing of edges.