Structure of a Maximal Total Independent Set

Lewis Stanton

Structure of a Maximal Total Independent Set

Combinatorics 2023-11-01 v3

Authors: Lewis Stanton

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.

Keywords

simple graph total independence number independence number edge independence number total independent set graph structure

Cite

@article{arxiv.2206.04395,
  title  = {Structure of a Maximal Total Independent Set},
  author = {Lewis Stanton},
  journal= {arXiv preprint arXiv:2206.04395},
  year   = {2023}
}

Comments

10 pages, Accepted version in Rose-Hulman Undergraduate journal

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