Spectral problem of fullerene vibrations

Rok vydání:	2020
Předmět:	Combinatorics Physics C++ string handling Multiplicity (mathematics) Circuit rank General Medicine Symmetry (geometry) Finite set Midpoint Truncated icosahedron Eigenvalues and eigenvectors
Zdroj:	Researches in Mathematics and Mechanics. 25:7-15
ISSN:	2519-206X
DOI:	10.18524/2519-206x.2020.1(35).221965
Popis:	Small vibrations of a graph of fullerene (truncated icosahedron) is considered each edge of which is a so-called Stieltjes string (a massless thread bearing finite number of point masses) symmetric with respect to its midpoint. The spectral problem is obtained by imposing the continuity and balance of forces conditions at the vertices. It is shown that when all the edges of the graph are the same then due to the symmetry of the problem there are multiple eigenvalues. The maximal multiplicity of an eigenvalue of such problem is 32, exactly the value which is maximal for cyclically connected graphs, i.e. $\mu+1$ where $\mu$ is the cyclomatic number of the graph.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::29cedf7faffcab09280d5c10e0fa571b https://doi.org/10.18524/2519-206x.2020.1(35).221965 Zobrazit plný text záznamu