Possible energy spectra of systems constructed from finite bethe lattices

Chu R. Kwang-Hua

Physica A: Statistical Mechanics and its Applications, 2019, vol. 527, issue C

Abstract: The exact polynomial equations related to the calculation for the spectra of networks with a local Cayley-tree-like structure are presented. We firstly obtain the adjacency matrix and the characteristic polynomial as well as the spectra for a k-regular graph or (finite) Bethe lattice with k=3 (the largest eigenvalue being around 5). After verification of k=3 results with those obtained previously we then predict the adjacency matrix and the characteristic polynomial as well as the spectra for a k-regular graph or (finite) Bethe lattice with k=9 (the largest eigenvalue being around 17) which are still challenging now and might be relevant to the Platonic tessellations of genus g≡4. Our approach could be applied to inclusion compounds formed between guest polymers and host systems.

Keywords: Energy; Dendrimer structure; Non-terminal vertex; Platonic tessellations (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:527:y:2019:i:c:s0378437119308167

DOI: 10.1016/j.physa.2019.121396

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