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# Copyright (c) 1997-2015
# Ewgenij Gawrilow, Michael Joswig (Technische Universitaet Berlin, Germany)
# http://www.polymake.org
#
# This program is free software; you can redistribute it and/or modify it
# under the terms of the GNU General Public License as published by the
# Free Software Foundation; either version 2, or (at your option) any
# later version: http://www.gnu.org/licenses/gpl.txt.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#-------------------------------------------------------------------------------
REQUIRE_EXTENSION bundled:graph_compare
CREDIT graph_compare = bundled:graph_compare
# @category Comparing
# true if //IncidenceMatrix1// and //IncidenceMatrix2// are isomorphic.
# @param IncidenceMatrix IncidenceMatrix1
# @param IncidenceMatrix IncidenceMatrix2
# @return Bool
# @depends bliss or nauty
# @example Compare the incidence matrices of the 2-dimensional cube and cross polytope:
# > $I1 = cube(2)->VERTICES_IN_FACETS;
# > $I2 = cross(2)->VERTICES_IN_FACETS;
# > print isomorphic($I1,$I2);
# | 1
user_function isomorphic(IncidenceMatrix, IncidenceMatrix) : c++ (include => "polymake/graph/compare.h");
# @category Comparing
# true if //graph1// and //graph2// are isomorphic.
# @param props::Graph graph1
# @param props::Graph graph2
# @return Bool
# @depends bliss or nauty
# @example Compare the vertex-edge graph of the square with the cycle graph on 4 nodes:
# > $g1 = cube(2)->GRAPH->ADJACENCY;
# > $g2 = cycle_graph(4)->ADJACENCY;
# > print isomorphic($g1,$g2);
# | 1
user_function isomorphic(props::Graph, props::Graph) : c++ (include => "polymake/graph/compare.h");
# @category Comparing
# Find the node permutation mapping //graph1// to //graph2//.
# If the given graphs are not isomorphic, throw an expection.
# @param props::Graph graph1
# @param props::Graph graph2
# @return Array<Int>
# @depends bliss or nauty
user_function find_node_permutation(props::Graph, props::Graph) : c++ (include => "polymake/graph/compare.h");
# @category Comparing
# Find the permutations mapping the non-symmetric incidence matrix //m1// to //m2//.
# If the given matrices are not isomorphic, throw an expection.
# @param IncidenceMatrix<NonSymmetric> m1
# @param IncidenceMatrix<NonSymmetric> m2
# @return Pair<Array<Int>,Array<Int>> ''first'' permutation applies to the rows, ''second'' applies to the columns
# @depends bliss or nauty
# @example > $m1 = new IncidenceMatrix([1,2],[5,3]);
# > $m2 = new IncidenceMatrix([4,3],[1,5]);
# > print find_row_col_permutation($m1,$m2);
# | <1 0> <0 1 4 3 5 2>
user_function find_row_col_permutation(IncidenceMatrix<NonSymmetric>, IncidenceMatrix<NonSymmetric>) \
: c++ (include => "polymake/graph/compare.h");
# @category Comparing
# Find the automorphism group of the graph.
# @param props::Graph graph
# @return Array<Array<Int>> each element encodes a node permutation.
# @depends bliss or nauty
# @example We first create the vertex-edge graph of the square and then print its automorphism group:
# > $g=new props::Graph(cube(2)->GRAPH->ADJACENCY);
# > print automorphisms($g);
# | 0 2 1 3
# | 1 0 3 2
# These two permutations generate the group of all node permutations
# that preserve vertex-edge connectivity.
user_function automorphisms(props::Graph) : c++ (include => "polymake/graph/compare.h");
# @category Comparing
# Find the order of the automorphism group of the graph.
# @param props::Graph graph
# @return Int the order of the automorphism group
# @depends bliss or nauty
# @example > print n_automorphisms(cycle_graph(5)->ADJACENCY);
# | 2
user_function n_automorphisms(props::Graph) : c++ (include => "polymake/graph/GraphIso.h");
# @category Comparing
# Find the automorphism group of the non-symmetric incidence matrix.
# @param IncidenceMatrix<NonSymmetric> m
# @return Array<Pair<Array<Int>,Array<Int>>> each element encodes a permutation of its rows (''first'') and columns (''second'').
# @depends bliss or nauty
# @example The group of combinatorial automorphisms of the 3-cube coincides with
# the group of (bipartite) graph automorphisms of the vertex/facet incidences.
# To print this group, type this:
# > print automorphisms(cube(3)->VERTICES_IN_FACETS);
# | (<0 1 4 5 2 3> <0 1 4 5 2 3 6 7>)
# | (<2 3 0 1 4 5> <0 2 1 3 4 6 5 7>)
# | (<1 0 2 3 4 5> <1 0 3 2 5 4 7 6>)
# This means that the group is generated by three elements, one per line in the output.
# Each is written as a pair of permutations. The first gives the action on the facets,
# the second the action on the vertices.
user_function automorphisms(IncidenceMatrix<NonSymmetric>) : c++ (include => "polymake/graph/compare.h");
# @category Comparing
# Find the automorphism group of the symmetric incidence matrix.
# @param IncidenceMatrix<Symmetric> m
# @return Array<Array<Int>> each element encodes a permutation of its rows (=columns).
# @depends bliss or nauty
user_function automorphisms(IncidenceMatrix<Symmetric>) : c++ (include => "polymake/graph/compare.h");
object Graph {
# @notest Rule defined "in stock" - currently without use
rule NodePerm.PERMUTATION : NodePerm.ADJACENCY, ADJACENCY {
$this->NodePerm->PERMUTATION=find_node_permutation($this->NodePerm->ADJACENCY, $this->ADJACENCY);
}
weight 5.10;
}
# Local Variables:
# mode: perl
# cperl-indent-level:3
# indent-tabs-mode:nil
# End:
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