Math Systems

Question 1

between two graphs means that they have essentially the same structure

Answer 1

ISOMORPHISM

Question 1

if you can combine two edges by deleting a vertex to combine two edges (or smoothing out the edges)and repeating the process

Answer 1

HOMOMORPHISM

Question 1

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

Question 2

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

Answer 2

algebraic system

Question 3

an algebraic system, denoted by (𝑆,⭑) , that consists a set 𝑆 with one binary operation ⭑ (read as “star”) which possesses certain properties

Answer 3

group

Question 3

Properties of a group

Answer 3

1. Closure
2. Associative
3. Identity
4. Inverse

Question 3

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

Answer 3

Closure Property

Question 4

if performing the operation on three elements by pairs will give the same answer even if the orde

Answer 4

Associative
Property

Question 5

The set 𝑆 has an identity or neutral element 𝑒 if for any element 𝑎 in S

Answer 5

Existence of
Identity (Neutral) Element

Question 6

Each of the elements in 𝑆 should have an inverse found in the same set

Answer 6

Existence
of Inverse Elements

Question 7

Symmetry groups are based on

Answer 7

regular
polygons

Question 8

refers to the degree with which an entity (object, function, etc) is invariant
under some geometric operation

Answer 8

Symmetry

Question 9

all of whose sides have the same length and all of whose angles have the same measure

Answer 9

regular
polygons

Question 10

Symmetry Groups

Answer 10

1. Identity
2. R120
3. R240
4. Rl
5. Rt
6. Rr

Question 11

dictates chemical bonding and spectroscopic properties

Answer 11

Molecular symmetry