On the largest eigenvalue of the distance matrix of a connected graph
Abstract
We report some properties of the largest eigenvalue Λ_{1} of the distance matrix of a connected graph, in particular, the upper and lower bounds for Λ_{1} involving the sum of the squares of the distances between all unordered pairs of vertices and the sum of the distances between a given vertex and all other vertices. We also give the relationship between Λ_{1} and the first Zagreb index and the Wiener index. Additionally, we give the NordhausGaddumtype result for Λ_{1}.
 Publication:

Chemical Physics Letters
 Pub Date:
 October 2007
 DOI:
 10.1016/j.cplett.2007.09.048
 Bibcode:
 2007CPL...447..384Z