The linespoints style (short form lp) connects adjacent points with straight line segments and then goes back to draw a small symbol at each point. Points are drawn with the default size determined by set pointsize unless a specific point size is given in the plot command or a variable point size is provided in an additional column of input data. Additional input columns may also be used to provide information such as variable line color. See lines and points.
Two keywords control whether or not every point in the plot is marked with a symbol, pointinterval (short form pi) and pointnumber (short form pn).
pi N or pi -N tells gnuplot to only place a symbol on every Nth point. A negative value for N will erase the portion of line segment that passes underneath the symbol. The size of the erased portion is controlled by set pointintervalbox.
pn N or pn -N tells gnuplot to label only N of the data points, evenly spaced over the data set. As with pi, a negative value for N will erase the portion of line segment that passes underneath the symbol.