Goldberg graphs are a name given in this work to the generalization of the Goldberg snarks of index 
,
7, 9, ... to all integers 
. They are illustrated above for 
to 7.
The Goldberg graphs of indices 
, 6, 7, 8, and 9 have graph
crossing number 10, 12, 14, 16, and 18, respectively (E. Weisstein, Oct. 1,
2026). These values suggest the conjecture that the
graph crossing number of the Goldberg graph
of index 
is 
for every integer 
.
Precomputed properties of Goldberg graphs are implemented in the Wolfram Language as GraphData[
"Goldberg", n
].
