On the dimension of a graph (1965)

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Link: https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/S0025579300005222

Abstract: 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 §2 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 0, denoted dim 0, as the minimum number $n$ such that $G$ can be embedded into Euclidean re-space $E_n$ with every edge of $G$ having length 1. The vertices of $G$ are mapped onto distinct points of $E_n$, but there is no restriction on the crossing of edges.

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