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#### Article Title

#### Abstract

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Let $G$ be a connected graph and let $w_1,\cdots w_r$ be a list of vertices. We refer the choice of a triple $(r;G;w_1,\cdots w_r)$, as a {\em metric selection.} Let $\rho$ be the shortest path metric of $G$. We say that $w_1,\cdots w_r$ {\em resolves $G$ (metricly)\/} if the function $c:V(G)\mapsto\bbz^r$ given by

\[ x\mapsto (\rho (w_1,x),\cdots ,\rho (w_r,x))\]

is injective. We refer to this function the {\em code map,} and to its image as the {\em codes\/} of the triple $(r;G;w_1,\cdots ,w_r)$.

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This paper proves basic results on the following questions:

\begin{enumerate}

\item What sets can be the image of a code map?

\item Given the image of a graph's code map, what can we determine about the graph?

\end{enumerate}

#### Recommended Citation

Feit, Paul
(2016)
"Classifying Resolving Lists by Distances between Members,"
*Theory and Applications of Graphs*:
Vol. 3:
Iss.
1, Article 7.

DOI: 10.20429/tag.2016.030107

Available at:
http://digitalcommons.georgiasouthern.edu/tag/vol3/iss1/7

*Supplemental Reference List with DOIs*