Abstract
This work addresses the existence question for weighted coherent configurations in the special case of rank 3, symmetric cc's, which are equivalent to strongly regular graphs, and weights of values ±1. Examples related to rank 3 group actions ofA5,S4(q) and PSL3(4) are discussed and a complete account of the regular full rank weights on the lattice graphL2(n) is given. These are found to be either trivial or tensor products of pairs of weights whose coboundaries are regular 2-graphs.
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