The sum of the squares of degrees: an overdue assignement

TL;DR

This paper provides a new, sharper asymptotic upper bound on the maximum sum of squared degrees in graphs with given vertices and edges, improving previous bounds for most cases.

Contribution

It introduces a concise, asymptotically sharp upper bound on f(n,m), enhancing earlier results by de Caen for nearly all graph parameters.

Findings

New asymptotically sharp upper bound on f(n,m)

Improves previous bounds for most n and m

Provides concise summary of earlier research

Abstract

Let f(n,m) be the maximum of the sum of the squares of degrees of a graph with n vertices and m edges. Summarizing earlier research, we present a concise, asymptotically sharp upper bound on f(n,m), better than the bound of de Caen for almost all n and m.