Abstract.

The Wiener index of a connected graph is the sum o f distances for all unordered pairs of

vertices. This is perhaps the mo st frequently used graph index in sciences, since Harold Wiener in 1947 obs erved that the Wiener index is closely correlated with the boiling points o f alkane molecules. We determine asymptotically the maximum Wiener index of planar triangulations and quadrangulations on n vertices. We do the same f or 4- and 5-connected triangulations and 3-connected quadrangulations as we ll. As triangulations are 3-connected and quadrangulations are 2-connected, the possibilities for connectivity are covered.

Exact conjectures are made for each of these problems, based on extensive computation. This is jo int work with Éva Czabarka, Peter Dankelmann and Trevor Olsen. DTSTAMP:20200926T010858Z DTSTART;TZID=Europe/Budapest:20190513T150000 DTEND;TZID=Europe/Budapest:20190513T160000 SEQUENCE:0 TRANSP:OPAQUE END:VEVENT END:VCALENDAR