The uniqueness of a Moore graph of degree 57 and diameter 2 is not known. See, for instance, this paper - http://www.sciencedirect.com/science/article/pii/S0024379509003735
- where they refer to `the missing Moore graph(s)' to indicate this fact.
Other discussion can be found here: http://symomega.wordpress.com/2009/09/11/i-want-more-moore-graphs/