Hartsfield and Ringel (1990) conjectured that every connected graph other than
is antimagic. Beaudoire et al. (2026) proved the conjecture for every graph
join of two finitesimple
graphs that each have at least one graph vertex,
provided the join has at least three vertices.
graph edges labeled bijectively
with 
so that the sums of the graph edge
labels at the graph vertices are pairwise distinct.
is antimagic. Beaudoire et al. (2026) proved the conjecture for every graph
join of two finite simple
graphs that each have at least one graph vertex,
provided the join has at least three vertices.
