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The dimension of a graph G is defined to be the minimum n such that G has a representation as a unit-distance graph in $${{\mathbb {R}}}^n$$Rn. In this article, we… Click to show full abstract
The dimension of a graph G is defined to be the minimum n such that G has a representation as a unit-distance graph in $${{\mathbb {R}}}^n$$Rn. In this article, we show that a dimension 6 graph with minimum edge-set has exactly 21 edges, with this minimum realized only in the case of the complete graph $$K_7$$K7. This result answers a higher-dimensional analogue of a question posed by Paul Erdős and presented by Alexander Soifer in The Mathematical Coloring Book.
Keywords:
minimum edge;
graph minimum;
graph;
dimension graph;
edge set
Journal Title: Graphs and Combinatorics
Year Published: 2017
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Journal Title: Graphs and Combinatorics
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!