Equality of distance packing numbers

We characterize the graphs for which the independence number equals the packing number. As a consequence we obtain simple structural descriptions of the graphs for which (i) the distance-kk-packing number equals the distance-2k2k-packing number, and (ii) the distance-kk-matching number equals the distance-2k2k-matching number. This last result considerably simplifies and extends previous results of Cameron and Walker (2005). For positive integers k1k1 and k2k2 with k1