Gromov hyperbolicity of periodic graphs Articles uri icon

publication date

  • June 2016

start page

  • S89

end page

  • S116

volume

  • 39

international standard serial number (ISSN)

  • 0126-6705

electronic international standard serial number (EISSN)

  • 2180-4206

abstract

  • Gromov hyperbolicity grasps the essence of both negatively curved spaces and discrete spaces. The hyperbolicity of a geodesic metric space is equivalent to the hyperbolicity of a graph related to it; hence, characterizing hyperbolic graphs is a main problem in the theory of hyperbolicity. Since this is a very ambitious goal, a more achievable problem is to characterize hyperbolic graphs in particular classes of graphs. The main result in this paper is a characterization of the hyperbolicity of periodic graphs.

keywords

  • periodic graphs; gromov hyperbolicity; infinite graphs; geodesics; planar graphs; constant; surfaces