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 graph of index 
has graph crossing number
5. The Goldberg graphs of indices 
through 12 have graph
crossing number 8, 10, 12, 14, 16, 18, 20, 22, and 24, respectively (E. Weisstein,
Oct. 3 and 5, 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
].
