Abstract
It is proved that if a graphG has maximum degreed, then its vertices can be represented by distinct unit vectors inR 2d so that two vectors are orthogonal if and only if the corresponding vertices are adjacent. As a corollary it follows that if a graph has maximum degreed, then it is isomorphic to a “unit distance graph” inR 2d.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Lovász, L.: On the Shannon capacity of graphs, IEEE Trans. Inf. Theory Vol. II 25,1, 1–7 (1979)
Maehara, H.: On the euclidean dimension of a complete multipartite graph, Discrete Math.72, 285–289 (1988)
Maehara, H.: Note on induced subgraphs of the unit distance graphE n, Discrete Comput. Geom.4, 15–18 (1989)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Maehara, H., Rödl, V. On the dimension to represent a graph by a unit distance graph. Graphs and Combinatorics 6, 365–367 (1990). https://doi.org/10.1007/BF01787703
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01787703