# Please do not post homework
# Lucy Martinez, 01-24-2025, Assignment 1

# Write a procedure AM(G) that inputs a graph [n,E]
# and outputs the adjacency matrix, represented as a list of length of lists
# of length n, such that M[i][j]=1 if {i,j} belongs to E and 0 otherwise.
# For example AM([2,{{1,2}}]); should output [[0,1],[1,0]]
AM:=proc(G) local L,s,i:
L:=[]:
for i from 1 to G[1] do
 L:=[op(L),[seq(0,i=1..G[1])]]:
od:

for s in G[2] do
  L[s[1],s[2]]:=1:
  L[s[2],s[1]]:=1:
od:
L:
end:




# Write a procedure Image(pi,G) that inputs a permutation pi of {1,...,n}
# and a graph G=[n,E] and outputs the image under pi
Image:=proc(pi,G) local i,s,E:
E:={}:
for s in G[2] do
 E:=E union {{pi[s[1]],pi[s[2]]}}:
od:
E:
end:



# By definition an unlabelled graph is an equivalence class of labeled graphs
# under graph isomorphism (i.e. mapping under the symmetric group).
# Write a procedure ULgraphs(n) that outputs a set of graphs
# with ONE member of each equivalence class.

# What is [seq(nops(ULgraphs(i)),i=1..6)] 
# Answer: 1, 2, 4, 11, 34, 156

# Is is in the OEIS? What is its A-number.
# Answer: A000088

ULgraphs:=proc(n):

end: