On the maximum CEI of graphs with paprameters

TL;DR

This paper characterizes the graphs with the maximum connective eccentricity index (CEI) within specific classes defined by fixed parameters such as connectivity, diameter, independence number, and minimum degree.

Contribution

It provides a complete characterization of the unique extremal graphs with maximum CEI for three classes based on fixed connectivity and other parameters.

Findings

Identifies graphs with maximum CEI for fixed connectivity and diameter.

Determines extremal graphs for fixed connectivity and independence number.

Finds graphs with maximum CEI for fixed connectivity and minimum degree.

Abstract

The connective eccentricity index (CEI) of a graph $G$ is defined as $\xi^{ce}(G)=\sum_{v \in V(G)}\frac{d_G(v)}{\varepsilon_G(v)}$, where $d_G(v)$ is the degree of $v$ and $\varepsilon_G(v)$ is the eccentricity of $v$. In this paper, we characterize the unique graphs with maximum CEI from three classes of graphs: the $n$-vertex graphs with fixed connectivity and diameter, the $n$-vertex graphs with fixed connectivity and independence number, and the $n$-vertex graphs with fixed connectivity and minimum degree.