Paper
Extremal Bounds on the Properties of Sigma and Albertson Indices for Non-Decreasing Degree Sequences
Authors
Jasem Hamoud, Duaa Abdullah
Abstract
In this paper, we establish bounds on the topological index -- the Sigma index -- focusing on analyzing the upper bound of its maximum value, which is known as , where is a class of graphs. We establish precise lower and upper bounds for the Sigma index by leveraging degree sequences , , and .
The minimum bound for the Albertson index related to the Sigma index bounds incorporates terms such as and . These results, rooted in extremal graph theory, enhance the understanding of topological indices in molecular and network analysis.