DessinGen.sagews

def Graf(S0, S1):
    D={} #empty graph
    G={} #edited graph that we add to
    verts={}
    #opening an empty graph
    graph=Graph(D, multiedges=True)

    #adds edges and vertices to the graph
    #S0 and S1 are lists of lists
def Dessin(S0, S1):
    numVertices = len(S0)+len(S1)

    #creating dictionary G of vertices with neighboring edges in counterclockwise order
    for i in range(numVertices):
        G[i]=(S0+S1)[i]

        verts[i]=[]
        #iterate over black vertices
    for i in range(len(S0)):
        #iterate over edges connected to black vertices
        for j in range(len(S0[i])):
            #iterate over white vertices
            for k in range(len(S1)):
                #check if black and white vertices have an edge in common
                if S0[i][j] in S1[k]:
                    #if they have an edge in common connect the vertices with the correct edge labeling
                    graph.add_edge(i,k+len(S0),S0[i][j])

    print('dictionary of neighboring edges:')
    print(G)

    #creating dictionary with vertices as keys and neighboring vertices in counterclockwise order
    for i in range(numVertices):
        for j in range(len(G[i])):
            for k in range(numVertices):
                if i!=k:
                    for l in range(len(G[k])):
                        if G[i][j] in G[k]:
                            if k not in verts[i]:
                                verts[i].append(k)

    #flip order of vertices so that we're counterclockwise.
    for i in range(len(verts)):
        L=[]
        for j in range(len(verts[i])):
            L.append(verts[i][(len(verts[i]))-j-1])
        verts[i]=L

    #all the vertices in S0 are black, all the vertices in S1 are white
    def color(S0, S1):
        grey=[]
        white=[]
        for i in range(len(S0)):
            grey.append(i)
        for i in range(len(S1)):
            white.append(i+len(S0))
        return [grey,white]

    #call and color the graph
    Dessin(S0, S1)
    color(S0, S1)

    #keep a certain ordering
    graph.set_embedding(verts)

    graph.graphplot(edge_labels=True, vertex_colors={'grey': color(S0,S1)[0],'white':color(S0,S1)[1]}, vertex_labels=True, edge_labels_background='transparent').show()
    return(graph)

####### Degree N=1
Graf([[1]],[[1]])


####### Degree N=2
Graf([[1,2]],[[1],[2]])

####### Degree N=3
# Graf([[1,3,2]],[[1],[2],[3]])     ##Wrong Direction
# Graf([[1],[2,3]],[[3],[1,2]])

####### Degree N=4
# Graf([[1,4,3,2]],[[1],[2],[3],[4]])    ##Doesn't Work
# Graf([[3],[1,4,2]],[[1],[2],[3,4]])
# Graf([[1,2],[3,4]],[[2],[4],[1,3]])
# Graf([[3],[1,4,2]],[[1,2],[3,4]])        ###MULTIEDGES
# Graf([[4],[1,3,2]],[[3],[1,4,2]])        ###MULTIEDGES
# Graf([[1,2],[3,4]],[[1,4],[2,3]])

####### Degree N=5
# Graf([[1,5,4,3,2]],[[1],[2],[3],[4],[5]])    ###Doesn't Work
# Graf([[4],[1,5,3,2]],[[1],[2],[3],[4,5]])
# Graf([[4,5],[1,3,2]],[[2],[3],[5],[1,4]])
# Graf([[3],[4],[1,5,2]],[[1],[2],[3,5,4]])    ###Wrong Vertices
# Graf([[1],[3],[2,5,4]],[[5],[1,2],[3,4]])
# Graf([[4],[1,2],[3,5]],[[2],[1,3],[4,5]])
# Graf([[4],[1,5,3,2]],[[3],[1,2],[4,5]])    ###MULTIEDGES
# Graf([[4],[1,2,5,3]],[[2],[1,3],[4,5]])    ###MULTIEDGES
# Graf([[3],[1,2,5,4]],[[2],[5],[1,4,3]])    ###MULTIEDGES
# Graf([[2,5],[1,4,3]],[[4],[1,5],[2,3]])    ###Wrong Vertices
# Graf([[1,4],[2,5,3]],[[2],[3],[1,4,5]])    ###MULTIEDGES
# Graf([[3,4],[1,2,5]],[[2],[4],[1,5,3]])    ###MULTIEDGES

####### Don't come out right
##Graf([[4],[1,2,5,3]],[[1],[2,3],[4,5]])
## Graf([[3,5],[1,4,2]],[[2],[3],[1,4,5]])

#Graf([[1,2,3,4],[5,6]],[[1,2],[4,5],[3,6]])    ###MULTIEDGES