The maximum Wiener index of maximal planar graphs
The maximum Wiener index of maximal planar graphs
Abstract The Wiener index of a connected graph is the sum of the distances between all pairs of vertices in the graph. It was conjectured that the Wiener index of an n -vertex maximal planar graph is at most $$\lfloor \frac{1}{18}(n^3+3n^2)\rfloor $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>⌊</mml:mo> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>18</mml:mn> </mml:mfrac> …