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The hierarchical product of graphs
dc.contributor.author | Barrière Figueroa, Eulalia |
dc.contributor.author | Comellas Padró, Francesc de Paula |
dc.contributor.author | Dalfó Simó, Cristina |
dc.contributor.author | Fiol Mora, Miquel Àngel |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV |
dc.date.accessioned | 2007-03-13T17:46:45Z |
dc.date.available | 2007-03-13T17:46:45Z |
dc.date.issued | 2007 |
dc.identifier.uri | http://hdl.handle.net/2117/672 |
dc.description.abstract | A new operation on graphs is introduced and some of its properties are studied. We call it hierarchical product, because of the strong (connectedness) hierarchy of the vertices in the resulting graphs. In fact, the obtained graphs turn out to be subgraphs of the cartesian product of the corresponding factors. Some well-known properties of the cartesian product, such as a reduced mean distance and diameter, simple routing algorithms and some optimal communication protocols are inherited by the hierarchical product. We also address the study of some algebraic properties of the hierarchical product of two or more graphs. In particular, the spectrum of the binary hypertree $T_m$ (which is the hierarchical product of several copies of the complete graph on two vertices) is fully characterized; turning out to be an interesting example of graph with all its eigenvalues distinct. Finally, some natural generalizations of the hierarchic product are proposed. |
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 | Representations of graphs |
dc.subject.other | Graph operation |
dc.subject.other | Hierarchical product |
dc.subject.other | Diameter |
dc.subject.other | Mean distance |
dc.subject.other | Adjacency matrix |
dc.subject.other | Eigenvalues |
dc.subject.other | Characteristic polynomial |
dc.title | The hierarchical product of graphs |
dc.type | Article |
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 | MTM2005-08990-C02-01 |
dc.relation.projectidctt | TEC2005-03575 |
local.personalitzacitacio | true |
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