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 \(m \leq 10\) or \(n \geq 8m^2 – 2m + 1\).