图的局部度量维数：广义层次积及其应用
Local metric dimension of graphs: generalized hierarchical products and some applications
摘要：
设$G$是一个图，而$S\subseteq V(G)$ .如果$G$的每两个邻顶点具有不同的度量$S$ -表示，则$S$是$G$的局部度量生成器。最小阶的局部度量生成元是$G$的局部度量基，它的阶是$G$的局部度量维数.证明了广义层次积的局部度量维数的上下界上界是精确的。结果被应用于确定或限制的几个重要的图形在数学化学的尺寸。利用该维度，提出了一种新的配送服务中客户编码分配模型。
英文摘要：
Let $G$ be a graph and $S\subseteq V(G)$. If every two adjacent vertices of $G$ have different metric $S$-representations, then $S$ is a local metric generator for $G$. A local metric generator of smallest order is a local metric basis for $G$, its order is the local metric dimension of $G$. Lower and upper bounds on the local metric dimension of the generalized hierarchical product are proved and demonstrated to be sharp. The results are applied to determine or bound the dimension of several graphs of importance in mathematical chemistry. Using the dimension, a new model for assigning codes to customers in delivery services is proposed.
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