Classical Hamming graphs are Cartesian products of complete graphs, and two
vertices are adjacent if they differ in exactly one coordinate. Motivated by
connections to unitary Cayley graphs, we consider a generalization where two
vertices are adjacent if they have no coordinate in common. Metric dimension of
classical Hamming graphs is known asymptotically, but, even in the case of
hypercubes, few exact values have been found. In contrast, we determine the
metric dimension for the entire diagonal family of 3-dimensional generalized
Hamming graphs. Our approach is constructive and made possible by first
characterizing resolving sets in terms of forbidden subgraphs of an auxiliary
edge-colored hypergraph.Comment: 19 pages, 7 figure