Classifying Resolving Lists by Distances between Members

Authors

Paul Feit, University of Texas of the Permian BasinFollow

Publication Date

2016

Abstract

Let G be a connected graph and let w₁,…w_r be a list of vertices. We refer the choice of a triple (r;G;w₁,…w_r), as a metric selection. Let ρ be the shortest path metric of G. We say that w₁,…w_r resolves G (metricly) if the function c:V(G) → ℤ^r given by

x → (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,…,w_r).

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?

Creative Commons License

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

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: https://digitalcommons.georgiasouthern.edu/tag/vol3/iss1/7