Antimagic labelling of graphs with maximum degree $Δ(G) = n - 4$
Abstract
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 $|E| \geq 7n$.
Fields of Study & Subjects
Graph Labeling and Dimension Problems
Advanced Graph Theory Research
Smarandache Functions and Recreational Number Theory
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 3 March 2026
- Language
- EN
- Document type
- Preprint