Ticket #13578: trac_13578-ringedtree.patch

new file sage/graphs/generators/families.py

@@ +1 @@
+r"""
+Families of graphs
+==================
+
+This file gathers generators for some families of graphs.
+- :meth:`RingedTree <GraphGenerators.RingedTree>`
+
+
+AUTHORS:
+
+- David Coudert (2012) Ringed Trees
+"""
+
+################################################################################
+#           Copyright (C) 2012 David Coudert <david.coudert@inria.fr>
+#
+# Distributed  under  the  terms  of  the  GNU  General  Public  License (GPL)
+#                         http://www.gnu.org/licenses/
+################################################################################
+
+# import from Python standard library
+from math import sin, cos, pi
+
+# import from Sage library
+from sage.graphs.graph import Graph
+
+
+def RingedTree(self, k):
+    r"""
+    Return the ringed tree on k-levels.
+
+    A ringed tree of level `k` is a fully binary tree with `k` levels (counting
+    the root as a level), in which all vertices at the same level are connected
+    by a ring. More precisely, we can use a binary string to represent each
+    vertex in the tree, such that the root (at level 0) is represented by an
+    empty string, and the left child and the right child of a vertex with string
+    `\sigma` are represented as `\sigma0` and \sigma1`, respectively. Then, at
+    each level `i = 1, 2, \cdots , k-1`, we connect two vertices `u` and `v`
+    represented by binary strings `\sigma_u` and `\sigma_v` if `(\sigma_u + 1)
+    \pmod{2^i}\equiv \sigma_v`, where the addition treats the binary strings as
+    the integers they represent.
+
+    INPUT:
+
+    - ``k`` -- the number of levels of the ringed tree.
+
+    EXAMPLE:
+
+        sage: G = graphs.RingedTree(5)
+        sage: P = G.plot(vertex_labels=False, vertex_size=10)
+        sage: P.show() # long time
+
+    TEST:
+
+        sage: G = graphs.RingedTree(-1)
+        Traceback (most recent call last):
+        ...
+        ValueError: The number of levels must be >= 1.
+    """
+    if k<1:
+        raise ValueError('The number of levels must be >= 1.')
+
+    E = []
+    W = {}
+    # We first add the tree edges
+    W[0] = ['']
+    for l in xrange(k-1):
+        W[l+1] = []
+        for r in W[l]:
+            E.append( (r,r+'0') )
+            E.append( (r,r+'1') )
+            W[l+1].append(r+'0')
+            W[l+1].append(r+'1')
+
+    # We then add the ring edges and fix positions of vertices for nice drawing
+    pos_dict = {'':(0,0.2)}
+    for l in xrange(1,k):
+        twol = 1<<l
+        r = 1 if l==1 else 1.5**l
+        theta0 = pi/twol
+        pos_dict[ W[l][twol-1] ] = ( r*sin(-theta0), r*cos(-theta0) )
+        if l>1: # to avoid adding twice edge ('0','1')
+            E.append( (W[l][0],W[l][twol-1]) )
+        for i in xrange(twol-1):
+            theta = (2*i+1)*theta0
+            pos_dict[ W[l][i] ] = ( r*sin(theta), r*cos(theta) )
+            E.append( (W[l][i],W[l][i+1]) )
+
+    return Graph(E, pos=pos_dict, name='Ringed Tree on '+str(k)+' levels' )
+

sage/graphs/graph_generators.py

@@ -173 +173 @@
 - :meth:`QueenGraph <GraphGenerators.QueenGraph>`
 - :meth:`RookGraph <GraphGenerators.RookGraph>`
 
+- :meth:`RingedTree <GraphGenerators.RingedTree>`
+
 
 Pseudofractal graphs
 --------------------
@@ -8655 +8657 @@
     QueenGraph = sage.graphs.generators.chessboard.QueenGraph
     RookGraph = sage.graphs.generators.chessboard.RookGraph
 
+    import sage.graphs.generators.families
+    RingedTree = sage.graphs.generators.families.RingedTree
+
 
 def canaug_traverse_vert(g, aut_gens, max_verts, property, dig=False, loops=False, implementation='c_graph', sparse=True):
     """