2024/08/21 by Grégoire Beaudoire, Beaudoire, Grégoire, Cédric Bentz +3
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2408.11931
openalex publication_date 2024/08/21 · openalex created_date 2024/12/20 · openalex updated_date 2026/07/28
An antimagic labelling of a graph is a bijection from the set of edges to \1, 2, … , 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 ≥ 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 ≥ 4 even, and to (k, 2)-bipartite biregular graphs for k ≥ 3 odd.