On the number of maximal independent sets in a graph

TL;DR

This paper revisits a classic graph theory problem by providing a new, simplified proof for the maximum number of maximal independent sets in an n-vertex graph, originally established by Miller, Muller, Moon, and Moser.

Contribution

The paper offers a new, straightforward proof of the known maximum number of maximal independent sets in graphs, simplifying previous arguments.

Findings

Confirmed the maximum number of maximal independent sets in an n-vertex graph

Provided a simpler proof of the classical result

Reinforced the understanding of graph independence structures

Abstract

Miller and Muller (1960) and independently Moon and Moser (1965) determined the maximum number of maximal independent sets in an $n$-vertex graph. We give a new and simple proof of this result.