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arXiv · 2408.11931

Antimagic labellings of (k, 2)-bipartite biregular graphs

Grégoire Beaudoire·Cédric Bentz·Christophe Picouleau
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Abstract

An antimagic labelling of a graph is a bijection from the set of edges to $\{1, 2, \ldots , m\}$, such that all vertex-sums are pairwise distinct, where the vertex-sum of a vertex is the sum of labels on the edges incident to it. We say a graph is antimagic if it has an antimagic labelling. In 2023, it has been proven that connected $(k, l)$-bipartite graphs are antimagic if $k \geq l + 2$ and one of k or l is odd. In this paper, we extend this result to connected $(k, 2)$-bipartite biregular graphs for $k \geq 4$ even, and to $(k, 2)$-bipartite biregular graphs for $k \geq 3$ odd.

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Grégoire Beaudoire, Cédric Bentz, Christophe Picouleau. 2024-08-21. Antimagic labellings of (k, 2)-bipartite biregular graphs. https://arxiv.org/abs/2408.11931

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