.. _cpp-graph/Automorphism:

**********************************************************
graph/Automorphism.hpp
**********************************************************
.. default-domain:: cpp
.. default-role:: cpp:expr

.. py:currentmodule:: mod
.. cpp:namespace:: mod


Class ``graph::Graph::Aut``
--------------------------------------------------------------------------------------------------------------------------------

.. class:: graph::Graph::Aut
    

    A class representing an automorphism of a :class:`Graph`.


Synopsis
^^^^^^^^

.. code-block:: c++
    
    struct Graph::Aut {
        Aut(std::shared_ptr<Graph> g, LabelType lt, bool withStereo, std::size_t i);
        Vertex operator[](Vertex v) const;
        MOD_DECL friend std::ostream &operator<<(std::ostream &s, const Aut &a);
    private:
        std::shared_ptr<Graph> g;
        LabelType lt;
        bool withStereo;
        std::size_t i;
    };

Details
^^^^^^^

.. cpp:namespace-push:: graph::Graph::Aut

.. cpp:function:: Vertex operator[](Vertex v) const

    :returns: the image of the given vertex under the permutation.

.. cpp:namespace-pop::


Class ``graph::Graph::AutGroup``
--------------------------------------------------------------------------------------------------------------------------------

.. class:: graph::Graph::AutGroup
    

    A class representing the automorphism group of a :class:`Graph`.


Synopsis
^^^^^^^^

.. code-block:: c++
    
    struct Graph::AutGroup {
        struct Gens {
            class iterator : public boost::iterator_facade<iterator, Aut, std::random_access_iterator_tag, Aut> {
                friend class Gens;
                iterator() = default;
                iterator(std::shared_ptr<Graph> g, LabelType lt, bool withStereo, std::size_t i);
            private:
                friend class boost::iterator_core_access;
                bool equal(const iterator &other) const;
                void increment();
                Aut dereference() const;
                std::size_t distance_to(const iterator &other) const;
                void advance(std::size_t n);
            private:
                std::shared_ptr<Graph> g;
                LabelType lt = LabelType::String;
                bool withStereo = false;
                std::size_t i = 0;
            };
            using const_iterator = iterator;
        private:
            friend class AutGroup;
            Gens(std::shared_ptr<Graph> g, LabelType lt, bool withStereo);
        public:
            iterator begin() const;
            iterator end() const;
            Aut operator[](std::size_t i) const;
            std::size_t size() const;
        private:
            std::shared_ptr<Graph> g;
            LabelType lt;
            bool withStereo;
        };
    public:
        AutGroup(std::shared_ptr<Graph> g, LabelSettings labelSettings);
        Gens gens() const;
        MOD_DECL friend std::ostream &operator<<(std::ostream &s, const AutGroup &a);
    private:
        std::shared_ptr<Graph> g;
        LabelType lt;
        bool withStereo;
    };

Details
^^^^^^^

.. cpp:namespace-push:: graph::Graph::AutGroup

.. function:: AutGroup(std::shared_ptr<const Graph> g, LabelSettings labelSettings)

.. function:: Gens gens() const

    :returns: a range of the generators for the group.

.. cpp:namespace-pop::


Class ``graph::Graph::AutGroup::Gens``
---------------------------------------------------------------

.. class:: graph::Graph::AutGroup::Gens


    A random-access range of the generators for the automorphism group.