Measurement Isomorphism of Graphs
Metric Geometry
2013-01-01 v1 Discrete Mathematics
Combinatorics
Abstract
The d-measurement set of a graph is its set of possible squared edge lengths over all d-dimensional embeddings. In this note, we define a new notion of graph isomorphism called d-measurement isomorphism. Two graphs are d-measurement isomorphic if there is agreement in their d-measurement sets. A natural question to ask is "what can be said about two graphs that are d-measurement isomorphic?" In this note, we show that this property coincides with the 2-isomorphism property studied by Whitney.
Keywords
Cite
@article{arxiv.1212.6551,
title = {Measurement Isomorphism of Graphs},
author = {Steven J. Gortler and Dylan P. Thurston},
journal= {arXiv preprint arXiv:1212.6551},
year = {2013}
}