Minimal Graphs with a Specified Code Map Image

Authors

Paul Feit, University of Texas of the Permian BasinFollow

Abstract

Let G be a graph and ^e1,…^en be n distinct vertices. Let ρ be the metric on G. The code map on vertices, corresponding to this list, is c(x)=(ρ (x,^e1),…ρ (x,^en)). This paper introduces a variation: begin with V ⊆ Ζ^n for some n, and consider assignments of edges E such that the identity function on V is a code map for G=(V,E). Refer to such a set E as a code-match.

An earlier paper classified subsets of V for which at least one code-match exists. We prove

• If there is a code-match E for which (V,E) is bipartite, than (V,E) is bipartite for every code-match E.
• If there is a code-match E for which (V,E) is a tree, then E is unique.
• There exists a code-match E such that (V,E) has a (2ⁿ-1}+1)-vertex-coloring.

Creative Commons License

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

Recommended Citation

Feit, Paul (2018) "Minimal Graphs with a Specified Code Map Image," Theory and Applications of Graphs: Vol. 5: Iss. 2, Article 4.
DOI: 10.20429/tag.2018.050204
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol5/iss2/4