Nonlocal metric dimension of graphs

DOI10.1007/S40840-022-01459-XarXiv2211.10614MaRDI QIDQ6417760

Dorota Kuziak, Sandi Klavžar

Publication date: 19 November 2022

Abstract: Nonlocal metric dimension ${mdim}_{mnell}(G)$ 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 ${mdim}_{mnell}(G)=1$ or with ${mdim}_{mnell}(G)=n(G)-2$ 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.

Mathematics Subject Classification ID

Combinatorial aspects of block designs (05B05) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Distance in graphs (05C12) Graph operations (line graphs, products, etc.) (05C76)

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