On the hierarchical product of graphs and the generalized binomial tree

In this article we follow the study of the hierarchical product of graphs, an operation recently introduced in the context of networks. A well-known example of such a product is the binomial tree which is the (hierarchical) power of the complete graph on two vertices. An appealing property of this s...

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Detalles Bibliográficos
Autores: Barrière, Lali, Comellas Padró, Francesc, Dalfó, Cristina, Fiol Mora, Miguel Ángel
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2009
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:10459.1/463304
Acceso en línea:https://doi.org/10.1080/03081080802305381
https://hdl.handle.net/10459.1/463304
Access Level:acceso abierto
Palabra clave:Graph
Hierarchical product
Binomial tree
Adjacency matrix
Eigenvalues
Eigenvectors
Descripción
Sumario:In this article we follow the study of the hierarchical product of graphs, an operation recently introduced in the context of networks. A well-known example of such a product is the binomial tree which is the (hierarchical) power of the complete graph on two vertices. An appealing property of this structure is that all the eigenvalues are distinct. Here we show how to obtain a graph with this property by applying the hierarchical product. In particular, we propose a generalization of the binomial tree and study some of its main properties.