Help:=proc(): print(`LT(n) , ST(n,G), Cycle(n), Wheel(n)`,NuST(n,G))
print(`DrawWheelGraph(n,G)`):
 end:

with(linalg):
with(combinat):
#LT(n):
LT:=proc(n) local A,a,i,j,paul:

#[[-a[{1,2}]-a[{1,3}]- .... -a[{1,n}], a[{1,2}],a[{1,3}], ..., a[{1,n}]

#[a[{1,2}], -a[{2,1}-a[{2,3}]- .... -a[{2,n}, a[{2,3}, a[{2,4}], ..., a[{2,n}]   ]
#...
#...
#...
#[a[{1,n}], a[{2,n}], ...., a[{n-1,n}], -a[{1,n}]- ... - a[{n-1,n}]


A:=  [seq([ seq(-a[{i,j}],j=2..i-1),

       add(a[{i,j}],j=1..n)-a[{i}],

        seq(-a[{i,j}],j=i+1..n)], i=2..n)]:
paul:=det(A);




{seq({seq(op(1,op(j,op(i,paul))),j=1..nops(op(i,paul)))},i=1..nops(paul))};

end:

#ST(n,G):The set of spanning trees on n vertices labeled
#1, ...,n of a a graph G, (given as a set of edges)
ST:=proc(n,G) local A,a,i,j,paul,NonEdges:

#[[-a[{1,2}]-a[{1,3}]- .... -a[{1,n}], a[{1,2}],a[{1,3}], ..., a[{1,n}]

#[a[{1,2}], -a[{2,1}-a[{2,3}]- .... -a[{2,n}, a[{2,3}, a[{2,4}], ..., a[{2,n}]   ]
#...
#...
#...
#[a[{1,n}], a[{2,n}], ...., a[{n-1,n}], -a[{1,n}]- ... - a[{n-1,n}]


A:=  [seq([ seq(-a[{i,j}],j=2..i-1),

       add(a[{i,j}],j=1..n)-a[{i}],

        seq(-a[{i,j}],j=i+1..n)], i=2..n)]:


NonEdges:={seq(seq({i,j},j=i+1..n),i=1..n)} minus G:

A:=expand(subs( { seq( a[edge]=0, edge in NonEdges) }, A)):
paul:=det(A);



{seq({seq(op(1,op(j,op(i,paul))),j=1..nops(op(i,paul)))},i=1..nops(paul))};

end:



Cycle:=proc(n) local i:
{seq({i,i+1},i=1..n-1),{1,n}}:
end:


Wheel:=proc(n) local i:
Cycle(n) union {seq({i,n+1},i=1..n)}:
end:



#NuST(n,G):The set of spanning trees on n vertices labeled
#1, ...,n of a a graph G, (given as a set of edges)
NuST:=proc(n,G) local A,a,i,j,NonEdges,edge:

#[[-a[{1,2}]-a[{1,3}]- .... -a[{1,n}], a[{1,2}],a[{1,3}], ..., a[{1,n}]

#[a[{1,2}], -a[{2,1}-a[{2,3}]- .... -a[{2,n}, a[{2,3}, a[{2,4}], ..., a[{2,n}]   ]
#...
#...
#...
#[a[{1,n}], a[{2,n}], ...., a[{n-1,n}], -a[{1,n}]- ... - a[{n-1,n}]


A:=  [seq([ seq(-a[{i,j}],j=2..i-1),

       add(a[{i,j}],j=1..n)-a[{i}],

        seq(-a[{i,j}],j=i+1..n)], i=2..n)]:


NonEdges:={seq(seq({i,j},j=i+1..n),i=1..n)} minus G:

A:=expand(subs( { seq( a[edge]=0, edge in NonEdges) }, A)):

A:=expand(subs( { seq( a[edge]=1, edge in G) }, A)):

det(A);
end: