Publication Date




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 $(r;G;w_1,\cdots ,w_r)$.


This paper proves basic results on the following questions:


\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?


Creative Commons License

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.

ref_tag2016030107.pdf (79 kB)
Supplemental Reference List with DOIs