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 inR2d 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” inR2d.
KeywordsUnit Vector Unit Distance Distance Graph Distinct Unit Unit Distance Graph
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