On a conjecture about edge irregular total labelings

Stephan Brandt, D. Rautenbach, J. Miškuf

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

As our main result, we prove that for every multigraph G = (V, E) which has no loops and is of order n, size m, and maximum degree Δ <10 m/√n there is a mapping f : V ∩ E → {1, 2, . . . , ⌈m+2/3⌉} such that f(u) + f(uv) + f(v) ≠ f(u′) + f(u′ V′) + f(V′) for every uv, u′v′ ∈ E with uv ≠ u′V. Functions with this property were recently introduced and studied by Bača et al. and were called edge irregular total labelings. Our result confirms a recent conjecture of Ivančo and Jendrol' about such labelings for dense graphs, for graphs where the maximum and minimum degree are not too different in terms of the order, and also for large graphs of bounded maximum degree.
Original languageEnglish
JournalJournal of Graph Theory
Volume57
Issue number4
Pages (from-to)333-343
Number of pages11
ISSN0364-9024
DOIs
Publication statusPublished - 2008

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