corona_product

corona_product(G, H)

Returns the Corona product of G and H.

The corona product of \(G\) and \(H\) is the graph \(C = G \circ H\) obtained by taking one copy of \(G\), called the center graph, \(|V(G)|\) copies of \(H\), called the outer graph, and making the \(i\)-th vertex of \(G\) adjacent to every vertex of the \(i\)-th copy of \(H\), where \(1 ≤ i ≤ |V(G)|\).

Parameters:

G, H: NetworkX graphs

The graphs to take the carona product of. G is the center graph and H is the outer graph

Returns:

C: NetworkX graph

The Corona product of G and H.

Raises:

NetworkXError

If G and H are not both directed or both undirected.

References

[1] M. Tavakoli, F. Rahbarnia, and A. R. Ashrafi,

“Studying the corona product of graphs under some graph invariants,” Transactions on Combinatorics, vol. 3, no. 3, pp. 43–49, Sep. 2014, doi: 10.22108/toc.2014.5542.

[2] A. Faraji, “Corona Product in Graph Theory,” Ali Faraji, May 11, 2021.

https://blog.alifaraji.ir/math/graph-theory/corona-product.html (accessed Dec. 07, 2021).

Examples

>>> G = nx.cycle_graph(4)
>>> H = nx.path_graph(2)
>>> C = nx.corona_product(G, H)
>>> list(C)
[0, 1, 2, 3, (0, 0), (0, 1), (1, 0), (1, 1), (2, 0), (2, 1), (3, 0), (3, 1)]
>>> print(C)
Graph with 12 nodes and 16 edges