Some properties of the Zagreb eccentricity indices
Keywords:Graph, first Zagreb eccentricity index, second Zagreb eccentricity index, diameter, eccentricity.
The concept of Zagreb eccentricity (E1 and E2) indices was introduced in the chemical graph theory very recently . The first Zagreb eccentricity (E1) and the second Zagreb eccentricity (E2) indices of a graph G are defined as
E1 = E1(G) = ∑vi ∈ V(G) ei2
E2 = E2(G) = ∑vivj ∈ E(G) ei ⋅ ej ,
where E(G) is the edge set and ei is the eccentricity of the vertex vi 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.
Special Issue Bled'11
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