05C50 Online Seminar: Rajesh Kannan

  • Date: 03/10/2023
  • Time: 08:00
Rajesh Kannan, Indian Institute of Technology Hyderabad (India)

University of Manitoba


On the Eccentricity Matrices of Trees: Invertibility, Inertia and Spectral Symmetry


The eccentricity matrix ε(G) of a connected graph G is obtained from the distance matrix of G by keeping the largest nonzero entries in each row and each column, and leaving zeros in the remaining ones. The eigenvalues of ε(G) are the ε-eigenvalues of G. It is well-known that the distance matrices of trees are invertible, and the determinant of such a matrix depend only on the number of vertices of the tree. We show that the eccentricity matrix of tree T is invertible if and only if either T is star or P_4. Also we show that any tree with odd diameter has 4 distinct ε-eigenvalues, and any tree with even diameter has the same number of positive and negative ε-eigenvalues (which is equal to the number of ’diametrically distinguished’ vertices). Finally, we will discuss trees with ε-eigenvalues that are symmetric with respect to the origin. This is joint work with Iswar Mahato.


The slides and a recording of this talk will be posted on the original website.


Stephen Kirkland, University of Manitoba 

Hermie Monterde, University of Manitoba

Other Information: 

The 05C50 Online is an international seminar about graphs and matrices held twice a month on Fridays.


Time: 8AM Pacific/10AM Central 


For more information, visit https://sites.google.com/view/05c50online/home


If you would like to attend, please register using this form to receive the zoom links: https://docs.google.com/forms/d/e/1FAIpQLSdQ98fh58cgeSWzbFe3t77i28FXDck1gYuX9jv_qd4kEf5l_Q/viewform?usp=sf_link