2026-04-17T14:04:30Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/11872025-07-17T13:30:01Zcom_2072_1033col_2072_452950

On the Hierarchical Product of Graphs and the Generalized Binomial Tree Barrière Figueroa, Eulalia Comellas Padró, Francesc de Paula Dalfó Simó, Cristina Fiol Mora, Miquel Àngel Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions Graph theory Binomial tree Hierarchical product Adjacency matrix Eignvalues Eigenvectors Grafs, Teoria de Classificació AMS::05 Combinatorics::05C Graph theory In this paper 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 some of its main properties are studied. 2007-09 Article https://hdl.handle.net/2117/1187 eng http://creativecommons.org/licenses/by-nc-nd/2.5/es/ Open Access Attribution-NonCommercial-NoDerivs 2.5 Spain 17 application/pdf