On the Euclidean dimension of a wheel (Q1101119)

The Euclidean dimension e(G) of a graph G is defined to be the minimum n so that G can be immersed in Euclidean n-space \(R^ n\) so that two distinct vertices of G are adjacent if and only if they are distance 1 apart. (The immersion need not be one-to-one on open arcs.) Constructive proofs are given to calculate e(G), for G a wheel \(W_{1,n}=K_ 1+C_ n,\) a complete tripartite graph, or a generalized wheel \(W_{m,n}=\bar K_ m+C_ n.\) For example: \(e(W_{1,6})=2\), \(e(W_{1,n})=3\) if \(n\neq 6\).