Why are the melting point and boiling point of graphite so remarkably high?
Because graphite is a non-molecular species.......
Graphite is a non-molecular material, and consists of an infinite array of carbon atoms bound together in two dimensions. Non-molecular substances typically have impossibly high melting and boiling points, and graphite is no exception. I suspect that the boiling point is so high that its measurement would be highly unreliable or non-existent.