On The Point-Distinguishing Chromatic Index of Complete Bipartite Graphs

Abstract

The point-distinguishing chromatic index of a graph $G$, denoted by ${\chi }_o(G)$, is the smallest number of colours in a (not necessarily proper) edge colouring of $G$ such that any two distinct vertices of $G$ are distinguished by sets of colours of their adjacent edges. The exact value of ${\chi }_o(K_{m,n})$ is found if either $m\le 10$ or $n\ge 8m^2–2m+1$.