A new formula for the generating function of the numbers of simple graphs

TL;DR

This paper introduces a novel formula for the generating function that counts simple graphs with n nodes, utilizing invariant theory to derive the result.

Contribution

It presents a new mathematical formula for the generating function of simple graphs, advancing combinatorial enumeration methods.

Findings

Derived a new formula for the generating function of simple graphs.

Applied invariant theory to combinatorial enumeration.

Provides a tool for counting simple graphs more efficiently.

Abstract

By using an approach of the invariant theory we obtain a new formula for the ordinary generating function of the numbers of the simple graphs with $n$ nodes.