For direct products of three complete graphs whose dimensions lie in the middle cone, the metric dimension and location-total-domination number of K(n+1) both equal 2(n3+1)-1.
Metric D imension of a D irect P roduct of T hree C omplete G raphs
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Metric Dimension of a Direct Product of Three Complete Graphs: The Middle Cone Family
For direct products of three complete graphs whose dimensions lie in the middle cone, the metric dimension and location-total-domination number of K(n+1) both equal 2(n3+1)-1.