Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:****Andrew Baxter**, Rutgers University, baxter{at} math [dot] rutgers [dot] edu**Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Maximizing the Wiener Index

Speaker: **Drew Sills**, Georgia Southern University

Date: Thursday, October 7, 2010 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

In 1947 and 1948, Harry Wiener published five papers which introduced a pair of graph theoretical invariants, one of which he called the "path number," but is now known instead as the Wiener index. The Wiener index was the first topological index to be introduced into the field of chemistry. It is widely studied to this day, and is now one of hundreds of topological indices of interest to chemists.

My talk is a preliminary report on a study of the conditions which give rise to the maximum possible Wiener index among all trees with a given degree sequence. This study is joint work with Hua Wang.

For those who attended Professor Zeilberger's birthday conference at Rutgers last May (or watched the youtube video), this talk is an expanded version of the 20-minute talk I gave then, incorporating new results and observations that have been found in the past few months.

No particular background will be assumed. All terms used in the talk will be carefully defined and explained, and accompanied by concrete examples. Students are particularly encouraged to attend!