Corona product

In graph theory, the corona product of graphs G and H, denoted ${\displaystyle G\circ H}$, can be obtained by taking one copy of G, called the center graph, and a number of copies of H equal to the order of G. Then, each copy of H is assigned a vertex in G, and that one vertex is attached to each vertex in its corresponding H copy by an edge.^[1]

The corona product ${\displaystyle G\circ H}$ of K₆ and C₄.

The star edge coloring of a graph G is a proper edge coloring without bichromatic paths and cycles of length four, similar to the star coloring of a graph, but coloring the edges instead of the vertices. The star edge chromatic index ${\displaystyle \chi '_{st}(G)}$ of the corona product of a path graph with cycle, wheel, helm and gear graphs are known.^[2]

See also

• Graph operations
• Graph product