I just ran across this delightful paper by an amazing triumvirate:

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> Paul Erdős, Frank Harary, and William Tutte. "On the dimension of a graph." *Mathematika* 12.118-122 (1965): 20.
>  ([Cambridge link](http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=6766352))
>  ([PDF download link](http://www.renyi.hu/~p_erdos/1965-09.pdf))
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>  ![EHTDefinition](https://i.stack.imgur.com/da7qH.png)
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They prove that $K\_n$ has dimension $n-1$, $K\_{n,n}$ has dimension $\le 4$,
and the dimension of the $n$-cube $Q\_n$ is $2$. And the Petersen graph has dimension $2$:

     ![Fig7](https://i.stack.imgur.com/GiVPc.png)

Surely there must have been advances on characterizing graphs according to this concept in the last ~half-century(!).
Can anyone provide some updates the status on this notion?

**Update**. Here is a modern, metrically accurate drawing of the Petersen graph:

   ![Petersen's](https://i.stack.imgur.com/5cVqo.png)

   (Image from [Wikipedia: *Unit Distance Graph*](http://en.wikipedia.org/wiki/Unit_distance_graph))