Abstract
In this paper we study the edge-clique cover number of the tensor product K n × K n . We derive an easy lowerbound for the edge-clique number of graphs in general. We prove that, when n is prime θ e (K n × K n ) matches the lowerbound. Moreover, we prove that θ e (K n × K n ) matches the lowerbound if and only if a projective plane of order n exists. We also show an easy upperbound for θ e (K n × K n ) in general, and give its limiting value when the Riemann hypothesis is true. © 2014 Springer International Publishing.