# cliqueNumber -- computes the clique number of a graph

## Synopsis

• Usage:
c = cliqueNumber G
• Inputs:
• G, ,
• Outputs:
• c, an integer, the clique number of G

## Description

cliqueNumber returns the clique number of a graph, the size of the largest clique contained in the graph. This number is also related to the dimension of the clique complex of the graph.

 i1 : R = QQ[a..d]; i2 : cliqueNumber completeGraph R o2 = 4 i3 : G = graph({a*b,b*c,a*c,a*d}) o3 = Graph{edges => {{a, b}, {a, c}, {b, c}, {a, d}}} ring => R vertices => {a, b, c, d} o3 : Graph i4 : cliqueNumber G o4 = 3 i5 : dim cliqueComplex G + 1 == cliqueNumber G o5 = true

## Ways to use cliqueNumber :

• "cliqueNumber(Graph)"

## For the programmer

The object cliqueNumber is .