Antimagic orientations of graphs with a dominating clique

Abdulrahman Al-Taweel

Antimagic orientations of graphs with a dominating clique

Combinatorics 2026-07-31 v1

Authors: Abdulrahman Al-Taweel

Abstract

A graph G with m edges has an antimagic orientation if its edges can be oriented and bijectively labelled 1, ..., m so that the oriented vertex sums, the labels on in-arcs minus the labels on out-arcs, are pairwise distinct. Hefetz, M\"utze and Schwartz conjectured that every connected graph admits an antimagic orientation. We prove that this conjecture holds for every graph with a dominating clique.

Keywords

antimagic orientation dominating clique graph labeling conjecture oriented vertex sums connected graph

Cite

@article{arxiv.2608.00209,
  title  = {Antimagic orientations of graphs with a dominating clique},
  author = {Abdulrahman Al-Taweel},
  journal= {arXiv preprint arXiv:2608.00209},
  year   = {2026}
}

Comments

6 pages, 1 figure