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dc.contributor.authorBarrière Figueroa, Eulalia
dc.contributor.authorComellas Padró, Francesc de Paula
dc.contributor.authorDalfó Simó, Cristina
dc.contributor.authorFiol Mora, Miquel Àngel
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV
dc.description.abstractA 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.rightsAttribution-NoDerivs 2.5 Spain
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
dc.subject.lcshRepresentations of graphs
dc.subject.otherGraph operation
dc.subject.otherHierarchical product
dc.subject.otherMean distance
dc.subject.otherAdjacency matrix
dc.subject.otherCharacteristic polynomial
dc.titleThe hierarchical product of graphs
dc.subject.lemacGrafs, Teoria de
dc.contributor.groupUniversitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions
dc.subject.amsClassificació AMS::05 Combinatorics::05C Graph theory
dc.rights.accessOpen Access

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