Total edge irregularity strength of complete graphs and complete bipartite graphs

A total edge irregular kk-labelling νν of a graph GG is a labelling of the vertices and edges of GG with labels from the set {1,…,k}{1,…,k} in such a way that for any two different edges ee and ff their weights φ(f)φ(f) and φ(e)φ(e) are distinct. Here, the weight of an edge g=uvg=uv is φ(g)=ν(g)+ν(u)+ν(v)φ(g)=ν(g)+ν(u)+ν(v), i. e. the sum of the label of gg and the labels of vertices uu and vv. The minimum kk for which the graph GG has an edge irregular total kk-labelling is called the total edge irregularity strength   of GG.We have determined the exact value of the total edge irregularity strength of complete graphs and complete bipartite graphs.