2025/03/19 by W. Li, Li, Wei-Tian, Yang, Po-Wen
Computer Science · Engineering · #05C78 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2503.15296
openalex publication_date 2025/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a graph on m edges, a bijective function between the edge set of the graph and \1,2,…,m\ is an antimagic labeling provided that when adding the labels of the edges incident to the same vertex, the sums are pairwise distinct. Hartsfield and Ringel conjectured that every connected graph has antimagic labeling. On the other hand, it is known that for any graph G, the disjoint union of G and many P3, a path on 3 vertices, is not antimagic. In this paper, we determined the exact number of P3's such that the disjoint union of a double star with the number of P3's is antimagic. In addition, we provide some examples of (1,1)-antimagic labelings. That is, the antimagic labelings have vertex sums 1 through the number of vertices of the graphs.