Some properties of the Zagreb eccentricity indices

The concept of Zagreb eccentricity (E-1 and E-2) indices was introduced in the chemical graph theory very recently [5, 12]. The first Zagreb eccentricity (E-1) and the second Zagreb eccentricity (E-2) indices of a graph G are defined as E-1 = E-1(G) = Sigma(vi is an element of V(G)) e(i)(2) and E-2 = E-2(G) = Sigma(vivj is an element of E(G)) e(i) . e(j) , where E(G) is the edge set and e(i) is the eccentricity of the vertex v(i) in G. In this paper we give some lower and upper bounds on the first Zagreb eccentricity and the second Zagreb eccentricity indices of trees and graphs, and also characterize the extremal graphs.