论文标题
图形的非局部度量维度
Nonlocal metric dimension of graphs
论文作者
论文摘要
非本地度量尺寸$ {\ rm DIM} _ {\ rm n \ ell}（g）的$ G $的$是作为最小的非局部分辨率集的基数，即，一组顶点分辨出每对$ g $的非附件的顶点。图形$ g $带有$ {\ rm dim} _ {\ rm n \ ell}（g）= 1 $或$ {\ rm dim} _ {\ rm n \ ell}（g）= n（g）= n（g）-2 $。针对块图，电晕产品和车轮确定非局部度量尺寸。证明了非局部度量维度上的两个上限。提出了任意图的嵌入到具有较小的非局部度量尺寸和小直径的超图中。
Nonlocal metric dimension ${\rm dim}_{\rm n\ell}(G)$ of a graph $G$ is introduced as the cardinality of a smallest nonlocal resolving set, that is, a set of vertices which resolves each pair of non-adjacent vertices of $G$. Graphs $G$ with ${\rm dim}_{\rm n\ell}(G) = 1$ or with ${\rm dim}_{\rm n\ell}(G) = n(G)-2$ are characterized. The nonlocal metric dimension is determined for block graphs, for corona products, and for wheels. Two upper bounds on the nonlocal metric dimension are proved. An embedding of an arbitrary graph into a supergraph with a small nonlocal metric dimension and small diameter is presented.
