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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有关图表中有限包装的更多信息

一组乙在图中的顶点的ģ称为ķ -有限包装如果为每个顶点v的ģ，其闭合附近具有至多ķ在顶点乙。所述ķ -有限装箱数的曲线图的G ^，记\（L_K（G）\） ，是顶点的最大数目ķ在-有限包装ģ。图的k限制堆积的概念是由Gallant等人介绍的，它是对图的众所周知的堆积的概括。在本文中，我们为k限制了图表的堆积数，分别根据其顺序，直径，周长和最大程度。结果，对于k限制的装箱数，我们得到了紧密的Nordhaus–Gaddum类型结果。最后，我们研究了树木的开放包装数，包装数和2极限包装数之间的关系。