Corona product
In graph theory, the corona product of graphs G and H, denoted , 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 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 of the corona product of a path graph with cycle, wheel, helm and gear graphs are known.[2]
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.[3]
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.[3]
See also
References
- ↑ Gomathi, P.; Murali, R. (2020). "Laceability Properties in Edge Tolerant Corona Product Graphs". TWMS Journal of Applied & Engineering Mathematics 10 (3): 734–741. ISSN 2146-1147.
- ↑ Kaliraj, K.; Sivakami, R.; Vivin, J. Vernold (2018). "Star Edge Coloring of Corona Product of Path and Wheel Graph Families". Proyecciones - Journal of Mathematics 37 (4): 593–608. doi:10.4067/S0716-09172018000400593. https://www.scielo.cl/pdf/proy/v37n4/0716-0917-proy-37-04-00593.pdf. Retrieved 2025-03-22.
- ↑ 3.0 3.1 De, Nilanjan (2017). "Application of Corona Product of Graphs in Computing Topological Indices of Some Special Chemical Graphs". Handbook of Research on Applied Cybernetics and Systems Science. IGI Global. pp. 82–101. doi:10.4018/978-1-5225-2498-4.ch004. ISBN 978-1-5225-2498-4.
External links
- Titus, P.; Subha, M.; Kumari, S. Santha (April 2023). "Monophonic graphoidal covering number of corona product graphs". Proyecciones - Journal of Mathematics (Antofagasta, Chile: Universidad Católica del Norte) 42 (2): 303-318. doi:10.22199/issn.0717-6279-4781. https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4781/4255.
- Putri, Rembulan; Suprajitno, Adirasari Herry; Susilowati, Liliek (January 2021). "The Dominant Metric Dimension of Corona Product Graphs". Baghdad Science Journal 18 (2): 349-??. doi:10.21123/bsj.2021.18.2.0349. ISSN 2078-8665. http://dx.doi.org/10.21123/bsj.2021.18.2.0349.
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