  We extend known results regarding the maximum rectilinear crossing number of
the cycle graph (C_n) and the complete graph (K_n) to the class of general
d-regular graphs R_{n,d}. We present the generalized star drawings of the
d-regular graphs S_{n,d} of order n where n+d= 1 mod 2 and prove that they
maximize the maximum rectilinear crossing numbers. A star-like drawing of
S_{n,d} for n = d = 0 mod 2 is introduced and we conjecture that this drawing
maximizes the maximum rectilinear crossing numbers, too. We offer a simpler
proof of two results initially proved by Furry and Kleitman as partial results
in the direction of this conjecture.
