A set B of vertices in a graph G is called a k-limited packing if for each vertex v of G, its closed neighbourhood has at most k vertices in B. The k-limited packing number of a graph G, denoted by L-k (G), is the largest number of vertices in a k-limited packing in G. The concept of the k-limited packing of a graph was introduced by Gallant et al., which is a generalization of the well-known packing of a graph. In this paper, we present some tight bounds for the k-limited packing number of a graph in terms of its order, diameter, girth, and maximum degree, respectively. As a result, we obtain a tight Nordhaus-Gaddum type result for the k-limited packing number. At last, we investigate the relationship among the open packing number, the packing number and 2-limited packing number of trees.
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