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