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arXiv · 2512.17693

Antimagicness of graphs with a dominating clique

Grégoire Beaudoire·Cédric Bentz·Christophe Picouleau
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Abstract

A graph $G = (V, E)$ is called antimagic if there exists a bijective labelling $f : E \rightarrow \{1, 2, \ldots, |E|\}$ such that the vertex-sums of labels over edges incident to a given vertex are all distinct. In this paper, we extend the antimagicness results over graphs with a dominating clique. We also introduce an alternative to the usual definition of antimagic graphs, called C-antimagic, allowing for the labelling to be injective in $\{1, 2, . . . , |E| + C\}$ instead of bijective, and show that almost all graphs with a dominating clique are 3-antimagic.

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Grégoire Beaudoire, Cédric Bentz, Christophe Picouleau. 2025-12-19. Antimagicness of graphs with a dominating clique. https://arxiv.org/abs/2512.17693

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