Total edge irregularity strength of large graphs
Copyright policy )Total edge irregularity strength of large graphs
Let $m:=|E(G)|$ sufficiently large and $s:=(m-1)/3$. We show that unless the maximum degree $Δ> 2s$, there is a weighting $w:E\cup V\to \{0,1,...,s\}$ so that $w(uv)+w(u)+w(v)\ne w(u'v')+w(u')+w(v')$ whenever $uv\ne u'v'$ (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.
14 pages
- University of Rostock Germany
total graph labeling, Signed and weighted graphs, Theoretical Computer Science, Graph labelling (graceful graphs, bandwidth, etc.), Total graph labeling, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Combinatorics (math.CO), Irregularity strength, 05C78
total graph labeling, Signed and weighted graphs, Theoretical Computer Science, Graph labelling (graceful graphs, bandwidth, etc.), Total graph labeling, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Combinatorics (math.CO), Irregularity strength, 05C78
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