mathematical systems Flashcards

1
Q

A

congruent geometric figures
(shapes that are exactly the same)

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2
Q

it is between 2 graphs means that they have essentially the same structure

A

isomorphism

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3
Q

what is homomorphism

A

combine 2 edges by deleting a vertex to combine the 2 edge (or soothing out the edges) and repeating the process until u make 2 graphs the same

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4
Q

_____ Theorem,
every non-planar graph has a subgraph that is homomorphic to the graphs ___ or ___

A

K5 or K3,3

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5
Q

K5

A

5 vertices
every vertex is connected to every other vertex

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6
Q

K3,3

A

bipartite graph
2 set of 3 vertices ach. every vertex from one set = form total of 9 edges

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7
Q

what are some practical applications of trying to draw a graph as a planar drawing

A

design of circuit boards (computers & other electronic components) - require wires to arranged in a planar drawing

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8
Q

S:
⋆:

A

S: set
⋆: one binary operation - combine 2 things to form a set to get a new thing (+)

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9
Q

what are the 4 properties of a group

A
  1. CLOSURE PROPERTY - sum of two integers is always an integer (For example, 3 + 5 = 8, which is an integer.)
  2. ASSOCIATIIVE PROPERTY - the associative property of addition holds true for the integers
    S, a ⋆ b ⋆ c = a ⋆ b ⋆ c
    - associative under addition
    - not associative under subtraction
  3. EXISTENCE OF IDENTITY (NEUTRAL)ELLEMENT - no. 0 serves as identity element for addition of integers. cos adding 0 to any integer does not change the integer (For example, 5 + 0 = 5.)
  4. EXISTANCEOF INVERSE ELEMENTS - inverse element is -a (For example, the inverse of 3 is -3, since 3 + (-3) = 0.)

we can conclude that the integers form a group under addition

In simple terms,
add integers, we get another integer (closure)
the order of adding numbers doesn’t matter (associativity)
adding 0 doesn’t change the number (identity)
every integer has an opposite that cancels it out (inverse)

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