Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4649256 | Discrete Mathematics | 2010 | 10 Pages |
Abstract
Some graphs admit drawings in the Euclidean plane (kk-space) in such a (natural) way, that edges are represented as line segments of unit length. We say that they have the unit distance property.The influence of graph operations on the unit distance property is discussed. It is proved that the Cartesian product preserves the unit distance property in the Euclidean plane, while graph union, join, tensor product, strong product, lexicographic product and corona do not. It is proved that the Cartesian product preserves the unit distance property also in higher dimensions.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Boris Horvat, Tomaž Pisanski,