Characterization of the hyperbolicity in the lexicographic product

Carballosa, Walter; Cruz, Amauris de la; Rodríguez, José M.

doi:10.1016/j.endm.2014.08.014

Cited by 1 publication

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“…The invariance of the hyperbolicity under some natural transformations on graphs have been studied in previous papers, for instance, removing edges of a graph is studied in [14,28]. Moreover, the hyperbolicity of some product graphs have been characterized: in [23,24,25,26,27,30,67] the authors characterize in a simple way the hyperbolicity of strong product of graphs, direct product of graphs, lexicographic product of graphs, Cartesian sum of graphs, graph join and corona, and Cartesian product of graphs. Some other authors have obtained results on hyperbolicity for particular classes of graphs: chordal graphs, vertex-symmetric graphs, bipartite and intersection graphs, bridged graphs and expanders [20,94,66,22,42,61,65].…”

Section: Introductionmentioning

confidence: 99%

Small values of the hyperbolicity constant in graphs

Bermudo

Rodrı́guez

Rosario

et al. 2016

Discrete Mathematics

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to my familyGracias a mis padres y hermanos por todo el apoyo y confianza desde que decidí emprender esta aventura, pero sobre todo por el infinito cariño y amor. A todos mis amigos que siempre han estado presentes de una u otra manera, gracias por ese gran apoyo moral y por sus palabras deánimo. La vida me ha dado tantos amigos que no acabaría de mencionarlos. Infinitas gracias. Conclusions Contributions of this work Open problems BibliographyNote that, if we consider a graph G whose edges have length equal to one and a graph G k obtained from G stretching out their edges until length k, then δ(G k ) = kδ(G). Therefore, all the results in this work can be generalized when the edges of the graph have length equal to k.

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