Fulek, RadoslavMoric, FilipPritchard, David2010-12-302010-12-302010-12-30201110.1016/j.disc.2010.11.006https://infoscience.epfl.ch/handle/20.500.14299/62541WOS:000287268100001The inverse degree of a graph is the sum of the reciprocals of the degrees of its vertices. We prove that in any connected planar graph, the diameter is at most 5/2 times the inverse degree, and that this ratio is tight. To develop a crucial surgery method, we begin by proving the simpler related upper bounds (4(vertical bar V vertical bar - 1) - vertical bar E vertical bar)/3 and 4 vertical bar V vertical bar(2)/3 vertical bar E vertical bar on the diameter (for connected planar graphs), which are also tight. (C) 2010 Elsevier B.V. All rights reserved.Planar graphDiameterInverse degreeConjecture-generating programSurgery argumentDiameter boundtext::journal::journal article::research article