Journal
DISCRETE MATHEMATICS
Volume 309, Issue 12, Pages 3871-3881Publisher
ELSEVIER
DOI: 10.1016/j.disc.2008.10.028
Keywords
Graph; Cartesian product; Hierarchical product; Diameter; Spectrum; Hamiltonian cycle; Coloring; Connectivity
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Funding
- Education and Science Ministry (Spain)
- European Regional Development Fund [MTM2005-08990-CO2-01, TEC2005-03575]
- Catalan Research Council [2005SGROO256]
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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. (C) 2008 Elsevier B.V. All rights reserved.
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