Biplanar Crossing Numbers and Random Graphs
László Székely
University of South Carolina http://people.math.sc.edu/laszlo 

Abstract 
Maximum Wiener index of planar triangulations and quadrangulations
The Wiener index of a connected graph is the sum of distances for all unordered pairs of vertices. This is perhaps the most frequently used graph index in sciences, since Harold Wiener in 1947 observed that the Wiener index is closely correlated with the boiling points of alkane molecules. We determine (asymptotically) the maximum Wiener index of planar triangulations and quadrangulations on n vertices. This is joint work with Eva Czabarka and Peter Dankelmann. 