Antimagic labelling of graphs with maximum degree $Δ(G) = n - 4$
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914365421125632 |
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| author | Beaudoire, Grégoire Bentz, Cédric Picouleau, Christophe |
| author_facet | Beaudoire, Grégoire Bentz, Cédric Picouleau, Christophe |
| contents | An antimagic labelling of a graph $G = (V,E)$ is a bijection from $E$ to $\{1,2, \ldots, |E|\}$, such that all vertex-sums are pairwise distinct, where the vertex-sum of each vertex is the sum of labels over edges incident to this vertex. A graph is said to be antimagic if it has an antimagic labelling. It has been proven that graphs $G$ with $Δ(G) \geq n - 3$ are antimagic, where $Δ(G)$ is the maximum degree of a vertex in $G$ and $n = |V|$. In this article, we extend this result to graphs with $Δ(G) = n - 4$, provided that $|E| \geq 7n$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_02956 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Antimagic labelling of graphs with maximum degree $Δ(G) = n - 4$ Beaudoire, Grégoire Bentz, Cédric Picouleau, Christophe Combinatorics An antimagic labelling of a graph $G = (V,E)$ is a bijection from $E$ to $\{1,2, \ldots, |E|\}$, such that all vertex-sums are pairwise distinct, where the vertex-sum of each vertex is the sum of labels over edges incident to this vertex. A graph is said to be antimagic if it has an antimagic labelling. It has been proven that graphs $G$ with $Δ(G) \geq n - 3$ are antimagic, where $Δ(G)$ is the maximum degree of a vertex in $G$ and $n = |V|$. In this article, we extend this result to graphs with $Δ(G) = n - 4$, provided that $|E| \geq 7n$. |
| title | Antimagic labelling of graphs with maximum degree $Δ(G) = n - 4$ |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2603.02956 |