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Title:	The generalized hierarchical product of graphs
Author:	Barrière Figueroa, Eulalia; Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel; Mitjana Riera, Margarida
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. COMBGRAF - Combinatòria, Teoria de Grafs i Aplicacions
Abstract:	A generalization of both the hierarchical product and the Cartesianproduct of graphs is introduced and some of its properties arestudied. We call it the generalized hierarchical product. In fact,the obtained graphs turn out to be subgraphs of the Cartesianproduct of the corresponding factors. Thus, some well-knownproperties of this product, such as a good connectivity, reducedmean distance, radius and diameter, simple routing algorithms andsome optimal communication protocols, are inherited by thegeneralized hierarchical product. Besides some of these properties,in this paper we study the spectrum, the existence of Hamiltoniancycles, the chromatic number and index, and the connectivity of thegeneralized hierarchical product.
Subject(s):	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
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