2026-04-13T15:10:48Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/19272025-07-17T10:01:00Zcom_2072_1033col_2072_452950

The generalized hierarchical product of graphs Barrière Figueroa, Eulalia Dalfó Simó, Cristina Fiol Mora, Miquel Àngel Mitjana Riera, Margarida Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions Graph coloring Hamiltonian systems Graph Cartesian product Hierarchical product Diameter Spectrum Hamiltonian cycles Coloring Connectivity Grafs, Teoria de Hamilton, Sistemes de Classificació AMS::05 Combinatorics::05C Graph theory A generalization of both the hierarchical product and the Cartesian product of graphs is introduced and some of its properties are studied. We call it the generalized hierarchical product. In fact, the obtained graphs turn out to be subgraphs of the Cartesian product of the corresponding factors. Thus, some well-known properties of this product, such as a good connectivity, reduced mean distance, radius and diameter, simple routing algorithms and some optimal communication protocols, are inherited by the generalized hierarchical product. Besides some of these properties, in this paper we study the spectrum, the existence of Hamiltonian cycles, the chromatic number and index, and the connectivity of the generalized hierarchical product. 2008-01 Article https://hdl.handle.net/2117/1927 eng http://creativecommons.org/licenses/by-nc-nd/2.5/es/ Open Access Attribution-NonCommercial-NoDerivs 2.5 Spain 15 pàgines application/pdf