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The local spectra of line graphs
dc.contributor.author | Fiol Mora, Miquel Àngel |
dc.contributor.author | Mitjana Riera, Margarida |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV |
dc.date.accessioned | 2007-04-02T13:40:29Z |
dc.date.available | 2007-04-02T13:40:29Z |
dc.date.issued | 2006-08 |
dc.identifier.uri | http://hdl.handle.net/2117/734 |
dc.description.abstract | 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 λl ∈ ev 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 o semiregular) graph G it derives from. Furthermore, some applications of this result are derived as, for instance, some results related to the number of cycles. |
dc.format.extent | 14 |
dc.language.iso | eng |
dc.rights | Attribution-NoDerivs 2.5 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nd/2.5/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs |
dc.subject.lcsh | Eigenvalues |
dc.subject.lcsh | Graph theory |
dc.subject.other | graph spectra |
dc.subject.other | eigenvalue |
dc.subject.other | local multiplicity |
dc.subject.other | line graph |
dc.title | The local spectra of line graphs |
dc.type | Article |
dc.subject.lemac | Valors propis |
dc.subject.lemac | Grafs, Teoria de |
dc.contributor.group | Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions |
dc.subject.ams | Classificació AMS::05 Combinatorics::05C Graph theory |
dc.rights.access | Open Access |
dc.relation.projectidctt | TEC-2005-03575 |
local.personalitzacitacio | true |
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