Characterization of $\alpha$-excellent $2$-trees

TL;DR

This paper investigates the properties of $ ext{alpha}$-excellent $2$-trees, providing new characterizations to better understand their structure and the conditions under which they are classified as such.

Contribution

The paper introduces two novel characterizations of $ ext{alpha}$-excellent $2$-trees, advancing the theoretical understanding of these graph classes.

Findings

Two new characterizations of $ ext{alpha}$-excellent $2$-trees

Enhanced understanding of the structural properties of $ ext{alpha}$-excellent $2$-trees

Theoretical framework for identifying $ ext{alpha}$-excellent $2$-trees

Abstract

A graph is $\alpha$-excellent if every vertex of the graph is contained in some maximum independent set of the graph. In this paper, we present two characterizations of the $\alpha$-excellent $2$-trees.