Gromov hyperbolicity in strong product graphs

Electronic Journal of Combinatorics

Volumn 20, Issue 3, 2013, Pages

  Carballosa, Walter ^a   Casablanca, Rocío M ^b   de la Cruz, Amauris ^a   Rodríguez, José M ^a  

^a UNIVERSIDAD CARLOS III DE MADRID   (Spain)

^b UNIVERSITY OF SEVILLE   (Spain)

Author keywords

Geodesics; Gromov hyperbolicity; Infinite graphs; Strong product graphs

Indexed keywords

EID: 84880618196     PISSN: None     EISSN: 10778926     Source Type: Journal    
DOI: 10.37236/3271     Document Type: Article

References (49)

1. Alvarez, V., Portilla, A., Rodríguez, J. M. and Tourís, E., Gromov hyperbolicity of Denjoy domains, Geom. Dedicata 121 (2006), 221-245.
2. Abajo, E., Casablanca, R. M., Diánez, A., García-Vázquez, P. The Menger number of the strong product of graphs, Discrete Math 313 (2013), 1490-1495.
3. Balogh, Z. M. and Buckley, S. M., Geometric characterizations of Gromov yperbolicity, Invent. Math. 153 (2003), 261-301.
4. Bermudo, S., Rodríguez, J. M. and Sigarreta, J. M., Computing the hyperbolicity constant, Comp. Math. Appl. 62 (2011), 4592-4595.
5. Bermudo, S., Rodríguez, J. M., Sigarreta, J. M. and Tourís, E., Hyperbolicity and complement of graphs, Appl. Math. Letters 24 (2011), 1882-1887.
6. Bermudo, S., Rodríguez, J. M., Sigarreta, J. M. and Vilaire, J.-M., Gromov hyperbolic graphs, Discrete Math. 313 (2013), 1575-1585.
7. Bonk, M., Heinonen, J. and Koskela, P., Uniformizing Gromov hyperbolic spaces. Astérisque 270 (2001).
8. Bowditch, B. H., Notes on Gromov's hyperobolicity criterion for path-metric spaces. Group theory from a geometrical viewpoint, Trieste, 1990 (ed. E. Ghys, A. Haeiger and A. Verjovsky; World Scientific, River Edge, NJ, 1991), 64-167.
9. Brinkmann, G., Koolen J. and Moulton, V., On the hyperbolicity of chordal graphs, Ann. Comb. 5 (2001), 61-69.
10. Cáceres, J., Hernando, C., Mora, M., Pelayo, I. M., Puertas, M. L., On the geodetic and the hull numbers in strong product graphs, Comput. Math. Appl. 60 (2010), 3020-3031.
11. Cantón, A., Granados, A., Pestana, D., Rodríguez, J. M., Gromov hyperbolicity of periodic planar graphs, to appear in Acta Math. Sinica.
12. Cantón, A., Granados, A., Pestana, D., Rodríguez, J. M., Gromov hyperbolicity of planar graphs, to appear in Central Europ. J. Math.
13. Carballosa, W., Pestana, D., Rodríguez, J. M. and Sigarreta, J. M., Distortion of the hyperbolicity constant of a graph, Electr. J. Comb. 19 (2012), #P67.
14. Carballosa, W., Portilla, A., Rodríguez, J. M. and Sigarreta, J. M., Gromov hyperbolicity of planar graphs and CW complexes. Submitted.
15. Carballosa, W., Rodríguez, J. M. and Sigarreta, J. M., New inequalities on the hyperbolity constant of line graphs, to appear in Ars Combinatoria.
16. Carballosa, W., Rodríguez, J. M., Sigarreta, J. M. and Villeta, M., On the Hyperbolicity Constant of Line Graphs, Electr. J. Comb. 18 (2011), #P210.
17. Chen, B., Yau, S.-T. and Yeh, Y.-N., Graph homotopy and Graham homotopy, Discrete Math. 241 (2001), 153-170.
18. Chepoi, V., Dragan, F. F., Estellon, B., Habib, M. and Vaxes Y., Notes on diameters, centers, and approximating trees of δ-hyperbolic geodesic spaces and graphs, Electr. Notes Discrete Math. 31 (2008), 231-234.
19. Frigerio, R. and Sisto, A.,Characterizing hyperbolic spaces and real trees, Geom. Dedicata 142 (2009), 139-149.
20. Ghys, E. and de la Harpe, P., Sur les Groupes Hyperboliques d'aprés Mikhael Gromov. Progress in Mathematics 83, Birkhäuser Boston Inc., Boston, MA, 1990.
21. G metrics, Proc. Amer. Math. Soc. 134 (2006), 1137-1142.
22. Hästö, P. A., Lindén, H., Portilla, A., Rodríguez, J. M. and Tourís, E., Gromov hyperbolicity of Denjoy domains with hyperbolic and quasihyperbolic metrics, J. Math. Soc. Japan 64 (2012), 247-261.
23. Hästö, P. A., Portilla, A., Rodríguez, J. M. and Tourís, E., Gromov hyperbolic equivalence of the hyperbolic and quasihyperbolic metrics in Denjoy domains, Bull. London Math. Soc. 42 (2010), 282-294.
24. Hästö, P. A., Portilla, A., Rodríguez, J. M. and Tourís, E., Comparative Gromov hyperbolicity results for the hyperbolic and quasihyperbolic metrics, Complex Var. Ellip. Eq. 55 (2010), 127-135.
25. Hästö, P. A., Portilla, A., Rodríguez, J. M. and Tourís, E., Uniformly separated sets and Gromov hyperbolicity of domains with the quasihyperbolic metric, Medit. J. Math. 8 (2011), 47-65.
26. Imrich, W. and Klavžar, S., Product Graphs: Structure and Recognition, Wiley Series in Discrete Mathematics and Optimization, (2000).
27. Jonckheere, E. and Lohsoonthorn, P., A hyperbolic geometry approach to multipath routing, Proceedings of the 10th Mediterranean Conference on Control and Automation (MED 2002), Lisbon, Portugal, July 2002. FA5-1.
28. Jonckheere, E. A., Controle du tra_c sur les reseaux a geometrie hyperbolique{Une approche mathematique a la securite de l'acheminement de l'information, J. Europ. de Syst. Autom. 37 (2003), 145-159.
29. Jonckheere, E. A. and Lohsoonthorn, P., Geometry of network security, American Control Conference ACC (2004), 111-151.
30. Jonckheere, E. A., Lohsoonthorn, P. and Ariaesi, F, Upper bound on scaled Gromovhyperbolic delta, Applied Mathematics and Computation 192 (2007), 191-204.
31. Jonckheere, E. A., Lohsoonthorn, P. and Bonahon, F., Scaled Gromov hyperbolic graphs, J. Graph Theory 2 (2007), 157-180.
32. Kaveh, A., Koohestani, K., Graph product for configuration processing of space structures, Comput. Struct. 86 (2008), 1219-1231.
33. Koolen, J. H. and Moulton, V., Hyperbolic Bridged Graphs, Europ. J. Comb. 23 (2002), 683-699.
34. Michel, J., Rodríguez, J. M., Sigarreta, J. M. and Villeta, M., Hyperbolicity an parameters of graphs, Ars Combinatoria 100 (2011), 43-63.
35. Michel, J., Rodríguez, J. M., Sigarreta, J. M. and Villeta, M., Gromov hyperbolicity in Cartesian product graphs, Proc. Indian Acad. Sci. Math. Sci. 120 (2010), 1-17.
36. Oshika, K., Discrete groups, AMS Bookstore, 2002.
37. Pestana, D., Rodríguez, J. M., Sigarreta, J. M. and Villeta, M., Gromov hyperbolic cubic graphs, Central Europ. J. Math. 10(3) (2012), 1141-1151
38. Portilla, A., Rodríguez, J. M., Sigarreta, J. M. and Vilaire, J.-M., Gromov hyperbolic tessellation graphs, to appear in Utilitas Math.
39. Portilla, A., Rodríguez, J. M. and Tourís, E., Gromov hyperbolicity through decomposition of metric spaces II, J. Geom. Anal. 14 (2004), 123-149.
40. Portilla, A. and Tourís, E., A characterization of Gromov hyperbolicity of surfaces with variable negative curvature, Publ. Mat. 53 (2009), 83-110.
41. Rodríguez, J. M., Characterization of Gromov hyperbolic short graphs, to appear in Acta Math. Sinica.
42. Rodríguez, J. M., Sigarreta, J. M., Vilaire, J.-M. and Villeta, M., On the hyperbolicity constant in graphs, Discrete Math. 311 (2011), 211-219.
43. Rodríguez, J. M. and Tourís, E., Gromov hyperbolicity through decomposition of metric spaces, Acta Math. Hung. 103 (2004), 53-84.
44. Rodríguez, J. M. and Tourís, E., A new characterization of Gromov hyperbolicity for Riemann surfaces, Publ. Mat. 50 (2006), 249-278.
45. Rodríguez, J. M. and Tourís, E., Gromov hyperbolicity of Riemann surfaces, Acta Math. Sinica 23 (2007), 209-228.
46. Sabidussi, G., Graph multiplication, Math. Z. 72 (1960), 446-457.
47. Špacapan, S., Connectivity of Strong Products of Graphs, Graphs Combin. 26 (2010), 457-467.
48. Sigarreta, J. M. Hyperbolicity in median graphs, to appear in Proc. Indian Acad. Sci. Math. Sci.
49. Tourís, E., Graphs and Gromov hyperbolicity of non-constant negatively curved surfaces. J. Math. Anal. Appl. 380 (2011), 865-881.