Corona product

[[File:Corona product.svg|thumb|upright=1.3|The corona product $G\circ H$ of [[complete graph|Template:Mvar]] and [[cycle graph|Template:Mvar]].]]

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

The star edge coloring of a graph Template:Mvar 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 $\chi {\text{'}}_{st}(G)$ of the corona product of a path graph with cycle, wheel, helm and gear graphs are known.

Applications

Corona products have applications in mathematical chemistry and the study of molecular graphs. In chemistry, molecules and molecular compounds are modeled as graphs where vertices represent atoms and edges represent chemical bonds. Corona product operations can be used to construct chemically interesting molecular graphs from simpler component graphs.

Topological indices are numerical graph invariants used to predict physico-chemical properties and biological activities of chemical compounds through quantitative structure–activity relationship (QSAR) and quantitative structure–property relationship (QSPR) studies. Various eccentricity-based topological indices of corona product graphs, including the total eccentricity index, eccentric connectivity index, and modified eccentric connectivity index, have been studied for molecular graph applications.

See also

• Graph operations
• Graph product

External links

• Template:Cite journal
• Template:Cite journal