As it is evident from the other answers, actually melting diamond, even assuming that the extreme conditions in which it could be obtained are achievable, would yield a liquid which would have nothing close to the properties of solid diamond. read more
Refer to this phase diagram of carbon. Unfortunately, this is a bit theoretical because the temperatures and pressures needed to investigate the properties of carbon are immense. read more
well.. you can melt a diamond, for sure. but when you melt it, it stops being a diamond. diamonds are a crystalline form of pure carbon. read more
But in a liquid, there is no fixed arrangement, so I don't think liquid carbon can be considered "diamond" or "graphite" or any other allotrope of carbon - it is just liquid carbon. That may be more semantics then the chemistry that you were looking for. read more
As the hardest known naturally occurring material, diamond can be used to polish, cut, or wear away any material, including other diamonds. Common industrial adaptations of this ability include diamond-tipped drill bits and saws, or use of diamond powder as an abrasive. read more