The Fifth Jump of the Point-Distinguishing Chromatic Index of \(K_{n,n}\)

The point-distinguishing chromatic index \(\chi_o(G)\) of a graph \(G\) represents the minimum number of colours in an edge colouring of \(G\) such that each vertex of \(G\) is distinguished by the set of colours of its incident edges. It is known that \(\chi_o(K_{n,n})\) is a non-decreasing function of \(n\) with jumps of value \(1\). We prove that \(\chi_o(K_{46,46}) = 7\) and \(\chi_o(K_{47,47}) = 8\).