, Volume 6, Issue 4, pp 365-367

On the dimension to represent a graph by a unit distance graph

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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.