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arXiv · 1212.6551

Measurement Isomorphism of Graphs

Steven J. Gortler·Dylan P. Thurston
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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.

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Steven J. Gortler, Dylan P. Thurston. 2012-12-28. Measurement Isomorphism of Graphs. https://arxiv.org/abs/1212.6551

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