# Corona product
> Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Corona_product
> Markdown URL: https://mediated.wiki/source/Corona_product.md
> Source: https://en.wikipedia.org/wiki/Corona_product
> Source revision: 1317023538
> License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/)
[[File:Corona product.svg|thumb|upright=1.3|The corona product of [{{mvar|K{{sub|6}}}}](/source/complete_graph) and [{{mvar|C{{sub|4}}}}](/source/cycle_graph).]]
In [graph theory](/source/graph_theory), the corona product of graphs {{mvar|G}} and {{mvar|H}}, denoted , can be obtained by taking one copy of {{mvar|G}}, called the center graph, and a number of copies of {{mvar|H}} equal to the [order](/source/order_(graph_theory)) of {{mvar|G}}. Then, each copy of {{mvar|H}} is assigned a vertex in {{mvar|G}}, and that one vertex is attached to each vertex in its corresponding {{mvar|H}} copy by an edge.[{{cite journal
| last1 = Gomathi
| first1 = P.
| last2 = Murali
| first2 = R.
| title = Laceability Properties in Edge Tolerant Corona Product Graphs
| journal = TWMS Journal of Applied & Engineering Mathematics
| volume = 10
| issue = 3
| pages = 734–741
| year = 2020
| issn = 2146-1147
}}]
The '''star edge coloring''' of a graph {{mvar|G}} is a proper edge coloring without bichromatic paths and cycles of length four, similar to the [star coloring](/source/star_coloring) of a graph, but coloring the edges instead of the vertices. The '''star edge chromatic index''' of the corona product of a path graph with cycle, wheel, helm and gear graphs are known.[{{cite journal
| last1 = Kaliraj
| first1 = K.
| last2 = Sivakami
| first2 = R.
| last3 = Vivin
| first3 = J. Vernold
| title = Star Edge Coloring of Corona Product of Path and Wheel Graph Families
| journal = Proyecciones - Journal of Mathematics
| volume = 37
| issue = 4
| pages = 593–608
| year = 2018
| doi = 10.4067/S0716-09172018000400593
| url = https://www.scielo.cl/pdf/proy/v37n4/0716-0917-proy-37-04-00593.pdf
| access-date = 2025-03-22
}}]
==Applications==
Corona products have applications in [mathematical chemistry](/source/mathematical_chemistry) and the study of [molecular graph](/source/molecular_graph)s. 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.[{{cite book
| last = De
| first = Nilanjan
| chapter = Application of Corona Product of Graphs in Computing Topological Indices of Some Special Chemical Graphs
| title = Handbook of Research on Applied Cybernetics and Systems Science
| publisher = IGI Global
| year = 2017
| pages = 82–101
| doi = 10.4018/978-1-5225-2498-4.ch004
| isbn = 978-1-5225-2498-4
}}]
[Topological indices](/source/Topological_index) 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](/source/eccentricity_index), eccentric connectivity index, and modified eccentric connectivity index, have been studied for molecular graph applications.