Multi-bridge graphs are anti-magic

Yu Bin Tai, Gek Ling Chia, Poh-Hwa Ong


An anti-magic graph  is a graph whose |E| edges  can be labeled with the first  |E| natural numbers such that each edge receives a distinct number and each vertex receives a distinct vertex sum which is obtained by taking the sum of the labels of all the edges incident to it. We prove that the multi-bridge graph is anti-magic.


r-bridge graph, anti-magic labeling, anti-magic graph

Full Text:




N. Alon, G. Kaplan, A. Lev, Y. Roditty, and R. Yuster, Dense graphs are antimagic, J. Graph Theory 47 (2004) 297–309.

K. Bérczi, A. Bernáth, and M. Vizer, Regular graphs are antimagic, Electron. J. Combin., 22 (2015) P3.34. F. Chang, Y.C. Liang, Z. Pan, and X. Zhu, Antimagic labeling of regular graphs, J. Graph Theory 82 (2016) 339–349.

D.W. Cranston, Regular bipartite graphs are antimagic, J. Graph Theory, 60 (2009) 173–182.

D.W. Cranston, Y.C. Liang, and X. Zhu, Regular graphs of odd degree are anti-magic, J. Graph Theory, 80 (2015) 28–33.

J.A. Gallian, A dynamic survey on graph labelings, Electron. J. Combin., (Dec 2021) # DS6.

N. Hartsfield and G. Ringel, Pearls in Graph Theory, Academic Press, Boston, (1990) 108–109.

G. Kaplan, A. Lev, and Y. Roditty, On zero-sum partitions and anti-magic trees, Discrete Math., 309 (2009) 2010–2014.

Y.C. Liang, T.L. Wong, and X. Zhu, Anti-magic labeling of trees, Discrete Math., 331 (2014) 9–14.

R. Simanjuntak, T. Nadeak, F. Yasin, K. Wijaya, N. Hinding, and K.A. Sugeng, Another Antimagic Conjecture, Symmetry, 13 (2021) 2071. https : //

T. Wang, Toroidal grids are anti-magic, Lecture Notes in Comput. Sci., 3595 (2005) 671–679.


  • There are currently no refbacks.

ISSN: 2338-2287

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

View EJGTA Stats