What are the properties of a group? All of the above I. Set S is closed under the operation ⋆ II. The associative property applies to the system III. There is an identity element in set S IV. Every element has an inverse in set S None of the above Cannot be determined

I. Set S is closed under the operation ⋆ II. The associative property applies to the system III. There is an identity element in set S IV. Every element has an inverse in set S

Graph Theory & Algebra Flashcards: Isomorphism, Groups, Planar Graphs

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Algebra - Abstract Algebra

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Cards in this deck(30)

___ between ___ graphs means that they have essentially the same structure.

Two graphs are _____ (or _____) if you can combine two edges by deleting a vertex to combine two edges (or smoothing out the edges) and repeating the process until you make two graphs the same.

A graph is said to be ____ if you can redraw the edges in a way that they do not crossover.

States that every non-planar graph has a subgraph that is homomorphic to the graphs K5 or K3,3.

Mathematical system consisting of a set of elements called the domain and one or more operations for combining the elements on the domain.

The set of real numbers with the operations of addition and multiplication are an example of this.

It is an algebraic system, denoted by (????,⋆), that consists a set ???? sith one binary operation ⋆ (read as "star") which possesses certain properties.

What are the properties of a group?

Means that if any two elements are combined using the operation, the result must be an element of the set

Associative in the set S if performing the operation on three elements by pairs will give the same answer even if the order of groupings by pairs is changed.

The set S has an identity or neutral element e if for any element a in S, ????⋆????=????⋆????=????

Each of the elements in ???? should have an inverse found in the same set. The idea of an inverse is that performing the binary operation ⋆ on an element with its inverse will give its identity.

What table is used to combine the elements/results when you let ???? = ????, ????, ???? and ⋆ the binary operation combining the elements in ?????

Every result is a member of the set ????. Therefore, the elements are closed with respect to ⋆

Set ???? has an identity (or neutral) element ????.

Each element in S has an inverse element.

The set is associative as illustrated by the following combinations of elements under ⋆.

Refers to the degree with which an entity (object, function, etc) is invariant under some geometric operation (such as rotation about an axis, reflection through a plane, and inversion about a point.)

Are based on regular polygons. A regular polygon all of whose sides have the same length and all of whose angles have the same measure.

What symmetry operation is this? ????

What symmetry operation is this? ????120

What symmetry operation is this? ????240

What symmetry operation is this? ????????

What symmetry operation is this?????????

This shows that the symmetry group under the operation Δ is not commutative

The number of symmetry groups in an regular ????-gon is given by?

Play an important role in the study of atomic reactions.

Dictates chemical bonding and spectroscopic properties.

Extremely powerful tool which simplifies the process of obtaining a variety of information about molecules.

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Graph Theory & Algebra Flashcards: Isomorphism, Groups, Planar Graphs

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