Geodesic
Trees Whose Even-Degree Vertices Induce a Path are Antimagic
Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 3, pp. 959-966.

Voir la notice de l'article provenant de la source Library of Science

An antimagic labeling of a connected graph G is a bijection from the set of edges E(G) to 1, 2, . . ., |E(G)| such that all vertex sums are pairwise distinct, where the vertex sum at vertex v is the sum of the labels assigned to edges incident to v. A graph is called antimagic if it has an antimagic labeling. In 1990, Hartsfield and Ringel conjectured that every simple connected graph other than K2 is antimagic; however the conjecture remains open, even for trees. In this note we prove that trees whose vertices of even degree induce a path are antimagic, extending a result given by Liang, Wong, and Zhu [Anti-magic labeling of trees, Discrete Math. 331 (2014) 9–14].
Keywords: antimagic labeling, tree 
@article{DMGT_2022_42_3_a16,
     author = {Lozano, Antoni and Mora, Merc\`e and Seara, Carlos and Tey, Joaqu{\'\i}n},
     title = {Trees {Whose} {Even-Degree} {Vertices} {Induce} a {Path} are {Antimagic}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {959--966},
     publisher = {mathdoc},
     volume = {42},
     number = {3},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2022_42_3_a16/}
}
TY  - JOUR
AU  - Lozano, Antoni
AU  - Mora, Mercè
AU  - Seara, Carlos
AU  - Tey, Joaquín
TI  - Trees Whose Even-Degree Vertices Induce a Path are Antimagic
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2022
SP  - 959
EP  - 966
VL  - 42
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2022_42_3_a16/
LA  - en
ID  - DMGT_2022_42_3_a16
ER  - 
%0 Journal Article
%A Lozano, Antoni
%A Mora, Mercè
%A Seara, Carlos
%A Tey, Joaquín
%T Trees Whose Even-Degree Vertices Induce a Path are Antimagic
%J Discussiones Mathematicae. Graph Theory
%D 2022
%P 959-966
%V 42
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2022_42_3_a16/
%G en
%F DMGT_2022_42_3_a16
Lozano, Antoni; Mora, Mercè; Seara, Carlos; Tey, Joaquín. Trees Whose Even-Degree Vertices Induce a Path are Antimagic. Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 3, pp. 959-966. http://geodesic.mathdoc.fr/item/DMGT_2022_42_3_a16/

[1] F.H. Chang, P. Chin, W.T. Li and Z. Pan, The strongly antimagic labelings of double spiders, (2017). arXiv:1712.09477

[2] G. Chartrand, L. Lesniak and P. Zhang, Graphs and Digraphs (CRC Press Boca Raton, 2011).

[3] K. Deng and Y. Li, Caterpillars with maximum degree 3 are antimagic, Discrete Math. 342 (2019) 1799–1801. https://doi.org/10.1016/j.disc.2019.02.021

[4] J.A. Gallian, Graph labeling, Electron. J. Combin. (2018) #DS6. https://doi.org/10.37236/27

[5] N. Hartsfield and G. Ringel, Pearls in Graph Theory (Academic Press INC., Boston, 1990) (revised version, 1994)

[6] G. Kaplan, A. Lev and Y. Roditty, On zero-sum partitions and anti-magic trees, Discrete Math. 309 (2009) 2010–2014. https://doi.org/10.1016/j.disc.2008.04.012

[7] Y.-Ch. Liang, T.-L. Wong and X. Zhu, Anti-magic labeling of trees, Discrete Math. 331 (2014) 9–14. https://doi.org/10.1016/j.disc.2014.04.021

[8] A. Lozano, M. Mora and C. Seara, Antimagic labelings of caterpillars, Appl. Math. Comput. 347 (2019) 734–740. https://doi.org/10.1016/j.amc.2018.11.043

[9] A. Lozano, M. Mora, C. Seara and J. Tey, Caterpillars are antimagic, (2018). arXiv:1812.06715

[10] J.L. Shang, Spiders are antimagic, Ars Combin. 118 (2015) 367–372.