Remarks on the sum of squares of eccentricity of graphs

Abstract

The sum of the squares of eccentricity (SSE), also called the first normalized Zagreb eccentricity index. In [19], the author compared the sum of square of eccentricity with the sum of square of degree, namely, the first Zagreb index (Mi-index) for chemical trees and two classes of connected graphs. In this note, we conduct our research along the same line as that of [19]. We construct infinite classes of graphs having larger sum of square of eccentricity than first Zagreb index, which in part answer a problem proposed by Zeng in [19].