# monomialGraph -- Returns a monomial graph

## Synopsis

• Usage:
G = monomialGraph(I,n)
• Inputs:
• I, , This monomial ideal be part of forming a quotient ring with respect to the ambient ring the ideal is in
• n, an integer, This integer determines the degree of monomials that will be considered
• Outputs:
• G, an instance of the type Graph, The monomial graph

## Description

The monomial graph with respect to a monomial ideal and an integer n is a graph with a vertex set of the monomials of the expression of the sum of the generators of the ambient ring for I to the power n. The edge set is formed by the rule that there is an edge between two of the vertices (which we are reminded are monomials) if and only if the degree of the least common multiple of the two vertices is n+1.

 i1 : R = QQ[x,y]; i2 : I = monomialIdeal (x^3, y^2*x); o2 : MonomialIdeal of R i3 : monomialGraph (I, 3) 2 o3 = Graph{x y => {}} 3 y => {} o3 : Graph