Total Vertex Irregularity Strength of Dense Graphs
Consider a graph of minimum degree ? 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.
total vertex irregularity strength dense graph order statistic vertex ordering 05c78 05c15