New bounds on domination and independence in graphs

TL;DR

This paper introduces new bounds for the domination and independence numbers in graphs using the Bhatia-Davis inequality, improving upon recent bounds and linking probabilistic inequalities with graph parameters.

Contribution

It presents novel bounds on graph domination and independence numbers derived from the Bhatia-Davis inequality, connecting probabilistic methods with graph theory.

Findings

Bounds compare favorably to recent ones

Utilizes Bhatia-Davis inequality for graph parameters

Provides tighter estimates for domination and independence numbers

Abstract

We propose new bounds on the domination number and on the independence number of a graph and show that our bounds compare favorably to recent ones. Our bounds are obtained by using the Bhatia-Davis inequality linking the variance, the expected value, the minimum, and the maximum of a random variable with bounded distribution.