An Isomorphism Problem in Z2

Authors

Matt Noble, Middle Georgia State UniversityFollow

Publication Date

2015

Abstract

We consider Euclidean distance graphs with vertex set ℚ² or ℤ² and address the possibility or impossibility of finding isomorphisms between such graphs. It is observed that for any distances d₁, d₂ the non-trivial distance graphs G(ℚ², d₁) and G(ℚ², d₂) are isomorphic. Ultimately it is shown that for distinct primes _p1, _p2 the non-trivial distance graphs G(ℤ², √p1) and G(ℤ², √p2) are not isomorphic. We conclude with a few additional questions related to this work.

Creative Commons License

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

Recommended Citation

Noble, Matt (2015) "An Isomorphism Problem in Z2," Theory and Applications of Graphs: Vol. 2: Iss. 1, Article 1.
DOI: 10.20429/tag.2015.020101
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol2/iss1/1