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On the hierarchical product of graphs and the generalized binomial tree. (English) Zbl 1225.05206

Summary: 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.

MSC:

05C76 Graph operations (line graphs, products, etc.)
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C05 Trees
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