The irregularity strength of \(K_{m,m}\) is 4 for odd m (Q1823264)

G. Chartrand et al. showed that for odd m, \(m\geq 3\), the edges of \(K_{m,m}\) can be labelled with 1, 2, 3, 4 in such a way that the (weighted) degrees of the vertices are all different. They conjectured that no such labelling exists with labels 1, 2, 3. In this note we prove this conjecture. G. Chartrand et al. showed that for odd m, \(m\geq 3\), the edges of \(K_{m,m}\) can be labelled with 1, 2, 3, 4 in such a way that the (weighted) degrees of the vertices are all different. They conjectured that no such labelling exists with labels 1, 2, 3. In this note we prove this conjecture.