Total Edge Irregularity Strength of Large Graphs

2010/06/23 by Florian Pfender, Pfender, Florian
Computer Science · Mathematics · #05C78 #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #Limits and Structures in Graph Theory #math.CO #msc:05C78

paper · pdf · doi:10.48550/arxiv.1006.4501

14 pages

arxiv created 2010/06/23 · openalex publication_date 2010/06/23 · arxiv updated 2010/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let m:=|E(G)| sufficiently large and s:=(m-1)/3. We show that unless the maximum degree Δ> 2s, there is a weighting w:E∪ V→ \0,1,...,s\ so that w(uv)+w(u)+w(v)≠ w(u'v')+w(u')+w(v') whenever uv≠ u'v' (such a weighting is called \em total edge irregular). This validates a conjecture by Ivanco and Jendrol' for large graphs, extending a result by Brandt, Miskuf and Rautenbach.

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