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