A new lower bound on the independence number of a graph

TL;DR

This paper establishes a new lower bound on the independence number of a connected graph based on its number of vertices and edges, improving understanding of graph independence properties.

Contribution

It introduces a novel lower bound formula for the independence number of connected graphs, advancing theoretical bounds in graph theory.

Findings

New lower bound formula for independence number

Applicable to all connected graphs

Enhances existing theoretical bounds

Abstract

For a given connected graph G on n vertices and m edges, we prove that its independence number is at least (2m+n+2-sqrt(sqr(2m+n+2)-16sqr(n)))/8.