The Fifth Jump of the Point-Distinguishing Chromatic Index of $K_{n,n}$

Abstract

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 ${\chi }_o(K_{47,47})=8$.