Abstract
Let G be a connected graph and let w1, · · ·wr be a list of vertices. We refer to the choice of a triple (r;G;w1, · · ·wr), as a metric selection. Let ρ be the shortest path metric ofG. We say that w1, · · ·wr resolves G (metricly) if the function c : V (G) −→ Z given by x 7→ (ρ(w1, x), · · · , ρ(wr, x)) is injective. We refer to c as the code map, and to its image as the codes of the triple (r;G;w1, · · · , wr). This paper proves basic results on the following questions: 1. What sets can be the image of a code map? 2. Given the image of a graph’s code map, what can we determine about the graph?
Highlights
M.A. Johnson and O.R. Oellermann Resolvability in graphs and the metric dimension of a graph, Disc.
R.A. Meltzer On the Metric dimension of a graph, Ars Combin.
Seara and D.R. Wood, Extremal graph theory for metric dimension and diameter, Electron.
Summary
M.A. Johnson and O.R. Oellermann Resolvability in graphs and the metric dimension of a graph, Disc.
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