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Characteristic Polynomial in Assessment of Carbon-Nano Structures
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Author(s): Sorana D. Bolboacă (Iuliu Haţieganu University of Medicine and Pharmacy, Romania)and Lorentz Jäntschi (Technical University of Cluj-Napoca, Romania & Babeş-Bolyai University, Romania & The University of Oradea, Romania)
Copyright: 2017
Pages: 26
Source title:
Sustainable Nanosystems Development, Properties, and Applications
Source Author(s)/Editor(s): Mihai V. Putz (West University of Timişoara, Romania & Research and Development National Institute for Electrochemistry and Condensed Matter (INCEMC) Timişoara, Romania)and Marius Constantin Mirica (Research and Development National Institute for Electrochemistry and Condensed Matter (INCEMC) Timişoara, Romania)
DOI: 10.4018/978-1-5225-0492-4.ch004
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Abstract
Six dodecahedrane assemblies as multiple of five and respectively six structures were constructed and investigated from the topological point of view. The investigation was conducted using characteristic polynomials, graph invariant encoding important properties of the graph of the chemical structure. The assemblies of 5, 6, 15 and 25 dodecahedranes proved to have the center in the same plane while the assemblies of 12 and 24 dodecahedranes degenerated from the planar central form to a chair conformation. Generally, the number of real roots of characteristic polynomials is equal to the number of atoms in the assembly. The obtained roots of the characteristic polynomial were split into intervals and the frequency apparition spectra were simulated. The obtained spectra were used to investigate the behavior of investigated assembly.
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