Abstract
The concept of Zagreb eccentricity ( E 1 and E 2 ) indices was introduced in the chemical graph theory very recently . 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 ) = ∑ v i ∈ V ( G ) e i 2 and E 2 = E 2 ( G ) = ∑ v i v j ∈ 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.
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