dc.contributor.author López Masip, Susana-Clara dc.contributor.author Muntaner Batle, F. A. dc.date.accessioned 2019-06-10T11:18:30Z dc.date.available 2019-06-10T11:18:30Z dc.date.issued 2015 dc.identifier.issn 0236-5294 dc.identifier.uri http://hdl.handle.net/10459.1/66433 dc.description.abstract Figueroa-Centeno et al. [4] introduced the following product of digraphs let D be a digraph and let Γ be a family of digraphs such that V (F) = V for every F∈Γ . Consider any function h:E(D)→Γ . Then the product D⊗hΓ is the digraph with vertex set V(D)×V and ((a,x),(b,y))∈E(D⊗hΓ) if and only if (a,b)∈E(D) and (x,y)∈E(h(a,b)) . In this paper, we deal with the undirected version of the ⊗h -product, which is a generalization of the classical direct product of graphs and, motivated by the ⊗h -product, we also recover a generalization of the classical lexicographic product of graphs, namely the ∘h -product, that was introduced by Sabidussi in 1961. We provide two characterizations for the connectivity of G⊗hΓ that generalize the existing one for the direct product. For G∘hΓ , we provide exact formulas for the connectivity and the edge-connectivity, under the assumption that V (F) = V , for all F∈Γ . We also introduce some miscellaneous results about other invariants in terms of the factors of both, the ⊗h -product and the ∘h -product. Some of them are easily obtained from the corresponding product of two graphs, but many others generalize the existing ones for the direct and the lexicographic product, respectively. We end up the paper by presenting some structural properties. An interesting result in this direction is a characterization for the existence of a nontrivial decomposition of a given graph G in terms of ⊗h -product. dc.description.sponsorship The research conducted in this document by the first author has been supported by the Spanish Research Council under project MTM2011-28800-C02-01 and by the Catalan Research Council under grant 2009SGR1387. dc.format.mimetype application/pdf dc.language.iso eng dc.publisher Springer dc.relation MICINN/PN2008-2011/MTM2011-28800-C02-01 dc.relation.isformatof Versió postprint del document publicat a https://doi.org/10.1007/s10474-015-0487-8 dc.relation.ispartof Acta Mathematica Hungarica, 2015, vol. 145, num. 2, p. 283-303 dc.rights (c) Springer, 2015 dc.rights (c) Akadémiai Kiadó, Budapest, 2015 dc.subject.classification Teoria de grafs dc.subject.other Graph theory dc.title Connectivity and other invariants of generalized products of graphs dc.type info:eu-repo/semantics/article dc.date.updated 2019-06-10T11:18:31Z dc.identifier.idgrec 028499 dc.type.version info:eu-repo/semantics/acceptedVersion dc.rights.accessRights info:eu-repo/semantics/openAccess dc.identifier.doi https://doi.org/10.1007/s10474-015-0487-8
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