Total Vertex Irregularity Strength of Dense Graphs
Piotr Majerski, Jakub Przybyło · Journal of Graph Theory · 2013
Abstract Consider a graph of minimum degree δ and order n . Its total vertex irregularity strength is the smallest integer k for which one can find a weighting such that for every pair of vertices of G . We prove that the total vertex irregularity strength of graphs with is bounded from above by . One of the cornerstones of the proof is a random ordering of the vertices generated by order statistics.