On the total vertex irregularity strength of trees

A vertex irregular total k-labelling λ:V(G)∪E(G)?{1,2,…,k} of a graph G is a labelling of vertices and edges of G done in such a way that for any different vertices x and y, their weights wt(x) and wt(y) are distinct. The weight wt(x) of a vertex x is the sum of the label of x and the labels of all edges incident with x. The minimum k for which a graph G has a vertex irregular total k-labelling is called the total vertex irregularity strength of G, denoted by . In this paper, we determine the total vertex irregularity strength of trees.