  We give a sharp lower bound on the lower $k$-limited packing number of a
general graph. Moreover, we establish a Nordhaus-Gaddum type bound on
$2$-limited packing number of a graph. Also, we investigate the concepts of
packing number ($1$-limited packing number) and open packing number in graphs
with more details. In this way, by making use of the classic result of Meir and
Moon (1975) and its total version (2005) we give new sharp upper bounds on
domination number and total domination number of trees.
