#OK to post homework 

#Zhizhang Deng, 12/03/2020, Assignment 18



1. 

    AllKConGraphs:=proc(n, k) local S,s,C:

    S:=AllGraphs(n):

    C:={}:



    for s in S do

     if nops(CCs(s))=k then

      C:=C union {s}:

     fi:

    od:



    C:

    end:



    NuKcomponentsGraphs:=proc(N, K) local n1:

        [seq( nops(AllKConGraphs(n1, K)),n1=1..N)]:

    end:



2. 

    AveNuCC := proc(n, K, M) local i, acc:

        acc := 0;

        for i from 1 to M by 1 do

            acc := acc + nops(CCs(RandGr(n, K)));

        end do: 

        acc := acc / M;

        return acc; 

    end: 



    seq(evalf(AveNuCC(30, 50, 1000)), i = 1 .. 5) = 1.763000000, 1.775000000, 1.804000000, 1.851000000, 1.818000000



    Pretty close. 



3. 

    EstimateCutOff := proc(n, M) local i: 

        for i from 1 to n*(n-1)/2 by 1 do

            if AveNuCC(n, i, M) < 1.05 then 

                return i; 

            end if;

        end do; 

        return FAIL; 

    end: