PreprintCC0arXiv
Antimagicness of join graphs
Abstract
An antimagic labelling of a graph G = (V,E) is a bijection from E to {1,2,...,|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 antimagic if it has an antimagic labelling. Hartsfield and Ringel in 1990 stated the celebrated conjecture: Every connected graph other than K_2 is antimagic. We prove the conjecture for join graphs with at least three vertices.
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BibTeX
@misc{beaudoire2026antimagicness,
title = {{Antimagicness of join graphs}},
author = {Grégoire Beaudoire and Cédric Bentz and Christophe Picouleau},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35245},
eprint = {2609.35245},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35245},
note = {CC0},
}
RIS
TY - UNPB
TI - Antimagicness of join graphs
AU - Grégoire Beaudoire
AU - Cédric Bentz
AU - Christophe Picouleau
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35245
UR - https://arxiv.org/abs/2609.35245
AB - An antimagic labelling of a graph G = (V,E) is a bijection from E to {1,2,...,|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 antimagic if it has an antimagic labelling. Hartsfield and Ringel in 1990 stated the celebrated conjecture: Every connected graph other than K_2 is antimagic. We prove the conjecture for join graphs with at least three vertices.
ER -