Structural characterization and spectral properties of hexagonal phenylene chain network
Department of Mathematics, University of Sialkot, 51310, Sialkot, Pakistan
2 Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan
Accepted: 17 April 2023
Published online: 17 May 2023
The spectrums of a molecule are used to calculate a bond length and strength between two atoms. This is based on the concept of electrostatic potential, which states that the energy of a given atom is minimized when the electrons in its outermost shell are evenly distributed. Spectrums also use to calculate the forces between two atoms, allowing chemists to accurately predict the bond lengths and strengths of molecules. The Kirchhoff index (KI) is a molecular invariant that measures the global connectivity of a chemical network. A higher KI indicates a more connected network, whereas a lower KI indicates a less connected network. Spanning trees in chemical networks have applications in a variety of areas, including drug design, materials science, and nanotechnology. By constructing a spanning tree, researchers can identify the most important bonds and interactions that hold a molecule together, and use this information to design new molecules with improved properties. The Kemeny’s constant can be utilized to predict the thermodynamic stability of molecules as well as determine the rate of a reaction. In this article, we have derived an exact expression for phenylene network. By employing a recursive connection, firstly we determined all the spectrums in relation to the corresponding Laplacian matrices. Secondly, we obtained the Kirchhoff index of phenylene network. Finally, we calculated spanning tress and Kemeny’s constant of phenylene network. Our computed results provide a comprehensive approach to study the different conformations of molecules and to determine the most stable conformation. These results will be helpful to determine the reactivity of molecules and will be useful to design new molecules by calculating these invariants between the atoms in desired molecule.
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