Let $n>1$ be an integer and $[n] = \{1,\ldots,n\}$. What is an example of non-isomorphic simple, undirected graphs $G\_i = ([n], E\_i)$ for $i=1,2$ with the following properties?


1. both $G\_1$ and $G\_2$ have [diameter](http://mathworld.wolfram.com/GraphDiameter.html) two,
2. $\chi(G\_1)=\chi(G\_2)$.



Non-isomorphic graphs with diameter two
$K\_n$ without edge and $K\_n$ without two edges which share a common vertex (well, if $n>3$). In both cases $\chi=n-1$.


