Python-Code

m=[(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(4,5)]
s=[[[1],[2],[3],[4],[5]]]
d=0
for i in range(len(m)):
    m.append((m[i][1],m[i][0]))
    
def wegcheck(x,y):
    u=0
    for i in range(len(m)):
        if (m[i][0],m[i][1])==(x[-1],y):
            u=u+1
    return(u)

def ungenutzt(x,y):
    a=1
    for p in range(len(x)-1):
        if (x[p],x[p+1])==(x[-1],y) or (x[p+1],x[p])==(x[-1],y):
            a=a+1
    return(a)

def möglich(x):
    u=[]
    for i in range(5):
        if wegcheck(x,i+1)!=0 and ungenutzt(x,i+1)==1:
            u.append(i+1)
    return(u)

while d<12:
    s.append([])
    for u in range(len(s[-2])):
        for k in range(len(möglich(s[-2][u]))):
            s[-1].append([])
            for ö in range(len(s[-2][u])):
                s[-1][-1].append(s[-2][u][ö])
            s[-1][-1].append(möglich(s[-2][u])[k])
            
    d=d+1

for ä in range(len(s[8])):
    print(s[8][ä])