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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. COMBGRAF - Combinatòria, Teoria de Grafs i Aplicacions
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.
Graph theory
Binomial tree
Hierarchical product
Adjacency matrix
Eignvalues
Eigenvectors
Grafs, Teoria de
Classificació AMS::05 Combinatorics::05C Graph theory
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
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