Geodesic
On the antimagic labeling of $(1,q)$-polar and $(1,q)$-decomposable graphs
Trudy Instituta matematiki, Tome 28 (2020) no. 1, pp. 98-108 
Vitaly Kalachev. On the antimagic labeling of $(1,q)$-polar and $(1,q)$-decomposable graphs. Trudy Instituta matematiki, Tome 28 (2020) no. 1, pp. 98-108. http://geodesic.mathdoc.fr/item/TIMB_2020_28_1_a9/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper the graphs yielded by the Algebraic Graph Decomposition theory are used to study the Hartsfield-Ringel conjecture on the antimagicness of connected graphs. This way some results on the conjecture are obtained, namely the antimagicness of connected $(1,2)$-polar and $(1,2)$-decomposable graphs, as well as connected $(1,q)$-polar and $(1,q)$-decomposable graphs satisfying some specific conditions.

[1] N. Hartsfield, G. Ringel, Pearls in Graph Theory, Academic Press, Inc., Boston, 1990 ; revised version, 1994 | MR | Zbl

[2] M. Barrus, “Antimagic labeling and canonical decomposition of graphs”, Information Processing Letters Journal, 110:7 (2010), 261–263 | DOI | MR | Zbl

[3] R. Tyshkevich, S. Suzdal, O. Maksimovich, R. Petrovich, “The Algebraic Graph Decomposition Theory”, Topics in Graph Theory, 2013, 145–170