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Journal of Combinatorial Theory Series A
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Journal of Combinatorial Theory Series A
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Every Graph Is an Integral Distance Graph in the Plane

Every graph is an integral distance graph in the plane
Authors: Norihide Tokushige; Katsuhiro Ota; Hiroshi Maehara;

Every Graph Is an Integral Distance Graph in the Plane

Abstract

For a finite subset of the plane the pairs of points for which their euclidean distance is an integer defines the corresponding integral distance graph. It is shown that every finite simple graph may be represented in such a way.

Keywords

euclidean plane, Distance in graphs, Elementary problems in Euclidean geometries, Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, integral distance graph oscillators, Planar graphs; geometric and topological aspects of graph theory, Theoretical Computer Science

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
5
Average
Top 10%
Average
hybrid