Further results on the sum of squares of eccentricity of graphs - Zeng, Ting, (Utilitas Mathematica, 2013)
The sum of the squares of eccentricity (SSE), also called the first normalized Zagreb eccentricity index. In [14], the authors compared the first and second normalized Zagreb eccentricity indices for trees and unicyclic graphs. In this paper, we study the problem of comparing the sum of square of eccentricity with the sum of square of degree (also called the first Zagreb index (Mi-index)). We prove that SSE is always greater than Aij-index for any chemical tree with at least three vertices, other than an exception. Moreover, we compare SSE with Mi-index for two classes of connected graphs.