An antimagic graph is a graph with graph edges labeled with distinct
elements sum of the graph edge labels at each graph
vertex differ.
Hartsfield and Ringel (1990) conjectured that every connected graph other than et al. (2026) proved the conjecture for every graph
join with at least three vertices .
See also Antimagic Square ,
Labeled Graph ,
Local Antimagic Chromatic
Number ,
Local Antimagic Graph ,
Local
Antimagic Labeling ,
Magic Graph
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References Beaudoire, G.; Bentz, C.; and Picouleau, C. "Antimagicness of Join Graphs." 28 Sep 2026. https://arxiv.org/abs/2609.35245 . Hartsfield,
N. and Ringel, G. Pearls
in Graph Theory: A Comprehensive Introduction. Referenced on Wolfram|Alpha Antimagic Graph
Cite this as:
Weisstein, Eric W. "Antimagic Graph."
From MathWorld https://mathworld.wolfram.com/AntimagicGraph.html
Subject classifications
graph edges labeled with distinct
elements 
so that the sum of the graph edge labels at each graph
vertex differ.
is antimagic. Beaudoire et al. (2026) proved the conjecture for every graph
join with at least three vertices.
