The cube of a graph is defined as its third graph power.

Since raising any graph to the power of its graph diameter gives a complete graph, the cube of any graph with
graph diameter is a complete graph.
Classes of such graphs include cocktail party
graphs, complete graphs, complete
bipartite graphs, complete tripartite
graphs, dipyramid graphs, star
graphs, and wheel graphs.

The following table summarizes the cube of some cube families of graphs.

## See also

Graph Power,

Graph
Product,

Graph Square
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## Cite this as:

Weisstein, Eric W. "Graph Cube." From
*MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/GraphCube.html

## Subject classifications