Abstract. The distance or D-eigenvalues of a graph G are the eigenvalues of its distance matrix. The distance or D-energy E D (G) of the graph G is the sum of the absolute values of its D-eigenvalues. Two graphs G 1 and G 2 are said to be

The Wiener index of a graph G, denoted by W (G) is the sum of the distances between all (unordered) pairs of vertices of G. In this paper, we obtain the Wiener index of line graphs and some class of graphs.

Let G be a simple graph with n vertices and m edges. For a vertex v i its eccentricity, e i is the largest distance from v i to any other vertices of G. In this paper we introduce the concept of eccentricity sum matrix ES(G) and eccentricity sum energy E ES (G) of a simple connected graph G and obtain bounds for eigenvalues of ES(G) and bounds for the eccentricity sum energy E ES (G) of a graph G.

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