A doublecross graph is a graph with graph crossing number 2.
The numbers of doublecross simple graphs on 
nodes are 0, 0, 0, 0, 0, 1, 39, ..., and the numbers of
connected graphs are 0, 0, 0, 0, 0, 1, 38, ....
Doublecross Graph
See also
2-Planar Graph, Graph Crossing Number, Planar Graph, Rectilinear Crossing Number, Singlecross GraphExplore with Wolfram|Alpha
References
Robertson, N.; Seymour, P.; Thomas, R. "Tutte's Edge-Colouring Conjecture." J. Combin. Th. 70, 166-183, 1997.Robertson, N.; Seymour, P. D.; and Thomas, R. "Girth Six Cubic Graphs Have Petersen Minors." Combinatorica 39, 1413-1423, 2019.Cite this as:
Weisstein, Eric W. "Doublecross Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DoublecrossGraph.html