Observability of Complete Multipartite Graphs with Equipotent Parts

Observability of a graph is the least \(k\) admitting a proper coloring of its edges by \(k\) colors in such a way that each vertex is identifiable by the set of colors of its incident edges. It is shown that for \(p \geq 3\) and \(q \geq 2\) the complete \(p\)-partite graph with all parts of cardinality \(q\) has observability \((p-1)q+2\).