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- W2048759904 abstract "Consider a graph $G=(V,E)$ of minimum degree $delta$ and order $n$. Its irregularity strength is the smallest integer $k$ for which one can find a weighting $w:Eto {1,2,ldots,k}$ such that $sum_{eni u}w(e) neq sum_{eni v}w(e)$ for every pair $u,v$ of vertices of $G$. In other words, it is just the maximum edge multiplicity required in an irregular multigraph whose underlying graph is $G$. We prove that the irregularity strength of graphs with $deltageq n^{0.5}ln n$ is bounded from above by $(4+o(1))frac{n}{delta}+4$. Our approach is based on a random ordering of the vertices of a graph suitable for applying a development of the algorithm used by Kalkowski, Karoński, and Pfender to prove the bound of $6leftlceilfrac{n}{delta}rightrceil$ for $deltageq 1$, which is the best upper bound thus far." @default.
- W2048759904 created "2016-06-24" @default.
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- W2048759904 date "2014-01-01" @default.
- W2048759904 modified "2023-10-14" @default.
- W2048759904 title "On the Irregularity Strength of Dense Graphs" @default.
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- W2048759904 doi "https://doi.org/10.1137/120886650" @default.
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