Date & Time: Friday, November 28, 2008, 16:00- 17:00.
Venue: Ramanujan Hall

Title: Distance Matrix of a Tree and Beyond

Speaker: Ravindra B. Bapat, Indian Statistical Institute, New Delhi

Abstract: Let T be a tree with n vertices. The distance matrix of T is an n × n matrix D with dij being the distance between vertices i and j, if i is not equal to j, and dii = 0. According to a classical result of Graham and Pollak, the determinant of D is a function only of n and does not depend on the tree. A formula for the inverse of D was obtained by Graham and Lovász. We discuss various recent extensions of these results. These include weighted versions, including matrix weights, a q-analogue and analogous results for the resistance distance.