Structure of a Total Independent Set

Authors

Lewis Stanton, University of SouthamptonFollow

Abstract

Let $G$ be a simple, connected and finite graph with order $n$. Denote the independence number, edge independence number and total independence number by $\alpha(G), \alpha'(G)$ and $\alpha''(G)$ respectively. This paper establishes an upper bound for $\alpha''(G)$ in terms of $\alpha(G)$, $\alpha'(G)$ and $n$. We also describe the possible structures for a total independent set containing a given number of elements.

Author Bio

Lewis Stanton completed this work in 2020 as part of a project in graph theory, and he graduated in 2022. He is now a PhD student in algebraic topology.

Faculty Sponsor

James Anderson

Recommended Citation

Stanton, Lewis (2023) "Structure of a Total Independent Set," Rose-Hulman Undergraduate Mathematics Journal: Vol. 24: Iss. 2, Article 8.
Available at: https://scholar.rose-hulman.edu/rhumj/vol24/iss2/8