The 
th-order
Menger sponge graph is the connectivity graph of cubes in the 
th iteration of the Menger sponge
fractal. The first two iterations are shown above.
The 
-Menger
sponge graph has 
vertices and 
edges.
Menger Sponge Graph
See also
Menger Sponge, Sierpiński Tetrahedron GraphExplore with Wolfram|Alpha
References
House of Graphs. Menger Sponge Graphs. Subdivided Cubical Graph.Referenced on Wolfram|Alpha
Menger Sponge GraphCite this as:
Weisstein, Eric W. "Menger Sponge Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MengerSpongeGraph.html