  A graph is diameter two edge-critical if its diameter is two and the deletion
of any edge increases the diameter. Murty and Simon conjectured that the number
of edges in a diameter two edge-critical graph on $n$ vertices is at most
$\lfloor \frac{n^{2}}{4} \rfloor$ and the extremal graph is the complete
bipartite graph $K_{\lfloor \frac{n}{2} \rfloor, \lceil \frac{n}{2} \rceil}$.
In the series papers [8-10], the Murty-Simon Conjecture stated by Haynes et al
is not the original conjecture, indeed, it is only for the diameter two
edge-critical graphs of even order. Haynes et al proved the conjecture for the
graphs whose complements have diameter three but only with even vertices. In
this paper, we prove the Murty-Simon Conjecture for the graphs whose
complements have diameter three, not only with even vertices but also odd ones.
