boolean_graph.cpython-39.pyc

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Boolean graphs
==============

The ``boolean_graph`` module defines
the ``BooleanGraph``  class,
which represents a Graph whose order is a power of 2.

AUTHORS:

- Paul Leopardi (2017-11-11): initial version

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    A Graph whose order is a power of 2.

    EXAMPLES:

    ::

        sage: from boolean_cayley_graphs.boolean_graph import BooleanGraph
        sage: g16 = BooleanGraph(16)
        sage: g16.order()
        16

    TESTS:

    ::

        sage: from boolean_cayley_graphs.boolean_graph import BooleanGraph
        sage: g16 = BooleanGraph(16)
        sage: print(g16)
        Graph on 16 vertices
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        A Graph whose order is a power of 2.

        EXAMPLES:

        ::

            sage: from boolean_cayley_graphs.boolean_graph import BooleanGraph
            sage: g16 = BooleanGraph(8)
            sage: g16.order()
            8
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        Check that the two BooleanGraphs ``self`` and ``other`` are isomorphic
        and that the isomorphism is given by a GF(2) linear mapping on the
        vector space of vertices.

        INPUT:

        - ``self`` -- the current object.
        - ``other`` -- another object of class BooleanFunctionImproved.
        - ``certificate`` -- bool (default False). If true, return a GF(2) matrix
           that defines the isomorphism.

        OUTPUT:

        If ``certificate`` is false, a bool value.
        If ``certificate`` is true, a tuple consisting of either (False, None)
        or (True, M), where M is a GF(2) matrix that defines the isomorphism.

        EXAMPLES:

        ::

            sage: from boolean_cayley_graphs.boolean_function_improved import BooleanFunctionImproved
            sage: from boolean_cayley_graphs.boolean_graph import BooleanGraph
            sage: bf1 = BooleanFunctionImproved([0,1,0,0])
            sage: cg1 = BooleanGraph(bf1.cayley_graph())
            sage: bf2 = BooleanFunctionImproved([0,0,1,0])
            sage: cg2 = BooleanGraph(bf2.cayley_graph())
            sage: cg1.is_linear_isomorphic(cg2)
            True
            sage: cg2.is_linear_isomorphic(cg1, certificate=True)
            (
                  [0 1]
            True, [1 0]
            )


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