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The metric dimension of a graph is the smallest number of nodes required toidentify all other nodes based on shortest path distances uniquely.Applications of metric dimension include discovering the source of a spread ina network, canonically labeling graphs, and embedding symbolic data inlow-dimensional Euclidean spaces. This survey gives a self-containedintroduction to metric dimension and an overview of the quintessential resultsand applications. We discuss methods for approximating the metric dimension ofgeneral graphs, and specific bounds and asymptotic behavior for deterministicand random families of graphs. We conclude with related concepts and directionsfor future work.

Getting the Lay of the Land in Discrete Space: A Survey of Metric Dimension and its Applications