Symmetry in Rhotrices and Rhomtree Applications for Hybrid Orbitals in Chemical Compounds

Authors

  • Trust Ovakaefe Utoyo Department of Mathematics, Federal University of Petroleum Resources, Effurun, Nigeria

Keywords:

Symmetric, Co-Minors, Transpose, Heart-Oriented, Heartless Rhotrix

Abstract

This work explores the application of the robust multiplication method of even dimensional rhotrices in determining the symmetric lines of some organic chemical compounds and graphical representation of energy distribution of some these compounds using rhomtrees. The co-minors of R2 and M2 rhotrices that produced a given symmetric pattern that analyzed the unique properties of even dimensional rhotrices were of great help. By partitioning the co-minors of these systems the underlying rhotrices were used to obtain the rhomtrees corresponding to the chemical compounds investigated, showing distribution pathways of energy bond using these abstract structures.

References

Ajibade, A. (2003). The concept of rhotrix in mathematical enrichment. International Journal of Mathematical Education in Science and Technology, 34, 175–179. https://doi.org/10.1080/0020739021000053828 Atanassov, K. T., & Shannon, A. G. (1998). Matrix-tertions and matrix-noitrets: Exercises in mathematical enrichment. International Journal of Mathematical Education in Science & Technology, 29(6). 898-903.

Cayley, A. (1889). A theorem on trees. Quarterly Journal of Mathematics, 23, 376–378. https://doi.org/10.1017/CBO9780511703799.010 Cayley. (1874). LVII. On the mathematical theory of isomers. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 47(314), 444-447.

Eschrig, H. (1989). Optimized LCAO method and the electronic structure of extended systems. Springer.

Isere, O. (2018b). Even-dimensional rhotrices. Notes on Number Theory and Discret Mathematics, 24(2), 125-133.https://doi.org/10.7546/nntdm.2018.24.2.125-133 Mohammed, A., & Sani, B. (2011). On construction of rhomtrees as graphical representation of rhotrices. Notes on Number Theory and Discrete Mathematics, 17(1), 21-29.

Sani, B. (2004). An alternative method for multiplication of rhotrices. International Journal of Mathematical Education in Science and Technology, 35(5), 777–781.

Utoyo, O. T., Isere, A. O., & Ugbene, I. J. (2023). A new multiplication approach with applications in differentiation and integration of even-dimensional hl rhotrices. Ambrose Alli University Journal of Physical and Applied Sciences, 3(1), 55–67.

Verma, S., & Singh, A. K. (2023). Rhotrix and its application in construction of balance incomplete block design. Journal of the African Mathematical Union and Springer-Verlag, 3(1). 756-765.

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Published

2025-03-31

How to Cite

Utoyo, T. O. (2025). Symmetry in Rhotrices and Rhomtree Applications for Hybrid Orbitals in Chemical Compounds. Faculty of Natural and Applied Sciences Journal of Applied Chemical Science Research, 2(2), 1–16. Retrieved from https://fnasjournals.com/index.php/FNAS-JACSR/article/view/651

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