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Symmetric graph. The Petersen graph is a (cubic) symmetric graph. Any pair of adjacent vertices can be mapped to another by an automorphism, since any five-vertex ring can be mapped to any other. In the mathematical field of graph theory, a graph G is symmetric (or arc-transitive) if, given any two pairs of adjacent vertices u1—v1 and u2—v2 ...
Symmetry occurs not only in geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that a mathematical object remains unchanged under a set of operations or transformations. [1] Given a structured object X of any sort, a symmetry is a mapping of the object onto itself which preserves the structure.
Symmetry (geometry) A drawing of a butterfly with bilateral symmetry, with left and right sides as mirror images of each other. In geometry, an object has symmetry if there is an operation or transformation (such as translation, scaling, rotation or reflection) that maps the figure/object onto itself (i.e., the object has an invariance under ...
The symmetry group of a snowflake is D 6, a dihedral symmetry, the same as for a regular hexagon. In mathematics, a dihedral group is the group of symmetries of a regular polygon, [1][2] which includes rotations and reflections. Dihedral groups are among the simplest examples of finite groups, and they play an important role in group theory and ...
In the theory of quadratic forms, the parabola is the graph of the quadratic form x 2 (or other scalings), while the elliptic paraboloid is the graph of the positive-definite quadratic form x 2 + y 2 (or scalings), and the hyperbolic paraboloid is the graph of the indefinite quadratic form x 2 − y 2. Generalizations to more variables yield ...
In mathematics, the symmetric difference of two sets, also known as the disjunctive union and set sum, is the set of elements which are in either of the sets, but not in their intersection. For example, the symmetric difference of the sets and is . The symmetric difference of the sets A and B is commonly denoted by (alternatively, ), , or .
A geometric shape or object is symmetric if it can be divided into two or more identical pieces that are arranged in an organized fashion. [ 5 ] This means that an object is symmetric if there is a transformation that moves individual pieces of the object, but doesn't change the overall shape. The type of symmetry is determined by the way the ...
Symmetric function. In mathematics, a function of variables is symmetric if its value is the same no matter the order of its arguments. For example, a function of two arguments is a symmetric function if and only if for all and such that and are in the domain of The most commonly encountered symmetric functions are polynomial functions, which ...