An iterative approach to graph irregularity strength

An assignment of positive integer weights to the edges of a simple graph GG is called irregular if the weighted degrees of the vertices are all different. The irregularity strength, s(G)s(G), is the maximal edge weight, minimized over all irregular assignments, and is set to infinity if no such assignment is possible. In this paper, we take an iterative approach to calculating the irregularity strength of a graph. In particular, we develop a new algorithm that determines the exact value s(T)s(T) for trees TT in which every two vertices of degree not equal to two are at distance at least eight.