Sigma index in Trees with Given Degree Sequences

TL;DR

This paper investigates the sigma index in trees with specified degree sequences, aiming to identify the structures that maximize this measure by building on prior characterizations of graphs with the highest sigma index.

Contribution

It extends the understanding of sigma index maximization to trees with given degree sequences, providing new characterizations and insights.

Findings

Identifies trees with maximum sigma index for given degree sequences

Provides a characterization of extremal trees in this class

Builds on previous work on sigma index in connected graphs

Abstract

The sigma index in graph theory refers to a measure of the degree differences between vertices in a graph. The goal is to determine the graphs that have the maximum sigma index within certain classes of graphs. Abdo, Dimitrov, and Gutman characterized the graphs with the greatest sigma index among all connected graphs of a fixed order.