**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 *d _{ij}* being the distance between vertices

*i*and

*j*, if

*i*is not equal to

*j*, and

*d*. According to a classical result of Graham and Pollak, the determinant of

_{ii}= 0*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.