Por favor, use este identificador para citar o enlazar este ítem:
http://hdl.handle.net/2117/735
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| Títulos: | The local spectra of regular line graphs |
| Autores: | Fiol Mora, Miquel Àngel
Mitjana Riera, Margarida |
| Otros autores: | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV
Universitat Politècnica de Catalunya. COMBGRAF - Combinatòria, Teoria de Grafs i Aplicacions |
| Palabras Clave: | /Àrees temàtiques de la UPC/Matemàtiques i estadística/Matemàtica discreta/Teoria de grafs
Eigenvalues
Graph theory
Graph spectrum
Eigenvalue
Local multiplicity
Line graph
Valors propis
Grafs, Teoria de
/Classificació AMS/05 Combinatorics/05C Graph theory |
| Resumen: | The local spectrum of a graph G = (V, E), constituted by the standard eigenvalues of G and their local multiplicities, plays a similar role as the global spectrum when the graph is “seen” from a given vertex. Thus, for each vertex i ∈ V , the i-local multiplicities of all the eigenvalues add up to 1; whereas the multiplicity of each eigenvalue λ of G is the sum, extended to all vertices, of its local multiplicities. In this work, using the interpretation of an eigenvector as a charge distribution on the vertices, we compute the local spectrum of the line graph LG in terms of the local spectrum of the regular graph G it derives from. Furthermore, some applications of this result are derived as, for instance, some results about the number of circuits of LG. |
| Aparece en las colecciones: | Documents de recerca
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