We report some properties of the largest eigenvalue Lambda(1) of the distance matrix of a connected graph, in particular, the upper and lower bounds for Lambda(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 Lambda(1) and the first Zagreb index and the Wiener index. Additionally, we give the Nordhaus-Gaddum-type result for Lambda(1). (C) 2007 Elsevier B.V. All rights reserved.