Function Repository Resource:

GraphPolynomial

Get the polynomial with coefficients giving the number of nonisomorphic graphs for a given number of vertices

Contributed by: Wolfram Staff (original content Sriram Pemmaraju and Steven Skienna)

ResourceFunction["GraphPolynomial"][n,x]

computes the polynomial in x for which the coefficient of x^m is the number of nonisomorphic graphs with n vertices and m edges.

ResourceFunction["GraphPolynomial"][n,x,"Directed"]

computes the polynomial with coefficients that count nonisomorphic directed graphs.

Examples

Compute a graph polynomial:

In[1]:=

Out[1]=

A graph polynomial for a directed graph:

In[2]:=

Out[2]=