The average distanceisnot morethan the independence number by Chung

@article{chung1988,
author = {F. Chung},
date = {1988},
journaltitle = {Journal of Graph Theory},
pages = {229--235},
title = {The average distanceisnot morethan the independence number},
volume = {12},
}

• maximum independent set upper bounds average distance by a linear function – [ed. paraphrased from another source] Let $G$ be a graph. Then $\bar{D} \le \alpha$, with equality holding if and only if $G$ is complete.