# completeGraph -- returns a complete graph

## Synopsis

• Usage:
K = completeGraph R
K = completeGraph(R,n)
K = completeGraph L
• Inputs:
• R, a ring
• n, an integer, number of variables to use
• L, a list, of vertices to make into a complete graph
• Outputs:
• K, , a complete graph on the vertices in L or on the variables of R

## Description

This function returns a special graph, the complete graph. The input specifies a set of vertices that will have the property that every vertex is adjacent to every other vertex. Non-specified vertices are treated as isolated vertices.
 `i1 : R = QQ[a,b,c,d,e];` ```i2 : completeGraph R o2 = Graph{edges => {{a, b}, {a, c}, {a, d}, {a, e}, {b, c}, {b, d}, {b, e}, {c, d}, {c, e}, {d, e}}} ring => R vertices => {a, b, c, d, e} o2 : Graph``` ```i3 : completeGraph(R,3) o3 = Graph{edges => {{a, b}, {a, c}, {b, c}}} ring => R vertices => {a, b, c, d, e} o3 : Graph``` ```i4 : completeGraph {a,c,e} o4 = Graph{edges => {{a, c}, {a, e}, {c, e}}} ring => R vertices => {a, b, c, d, e} o4 : Graph```