# Diameter Bounds for Planar Graphs - Mathematics > Combinatorics

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Abstract: The inverse degree of a graph is the sum of the reciprocals of the degrees ofits vertices. We prove that in any connected planar graph, the diameter is atmost 5-2 times the inverse degree, and that this ratio is tight. To develop acrucial surgery method, we begin by proving the simpler related upper bounds4V-1-E-3 and 4V^2-3E on the diameter for connected planar graphs, whichare also tight.

Author: ** Radoslav Fulek, Filip MoriÄ‡, David Pritchard**

Source: https://arxiv.org/