Structure of a Maximal Total Independent Set

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 $\alpha (G),{\alpha }^{\prime }(G)$ and $\alpha "(G)$ respectively. This paper establishes a relation between $\alpha "(G)$ with $\alpha (G)$, ${\alpha }^{\prime }(G)$ and $n$. It also describes the possible structures of a total independent set of a given size.

arXiv comment10 pages, Accepted version in Rose-Hulman Undergraduate journal