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GM > Unit2HOLIDAYREVISEFROEXAMSA+NEEDBYTERM4 > Flashcards

Unit2HOLIDAYREVISEFROEXAMSA+NEEDBYTERM4 Flashcards

1
Q

Vertex

A

How many pints there are e.g. a,b,c,d connect to make a graph, so there are 4 points.

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2
Q

Isolated vertex

A

not connected to nay vertex.

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3
Q

Connected vertex

A

Has every vertex connected to every other vertex either either directly or indirectly via other vertices.

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4
Q

Adjacency matrix

A

Mathematical representation of a diagram:
- 0= no direct connection.
- 1’s in diagonal=loop
- column all 0’s= isolated vertex.

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5
Q

Planar graph

A

Graphs that can be drawn with no overlapping edges. They follow the Euler’s formula: v-e+f=2

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6
Q

Isomorphic graph

A
  • The same graph drawn in a different way.
  • Same no of edges and vertices and the corresponding vertices have the same degree and the edges connect the same vertices.
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7
Q

Complete graph

A
  • A network where all vertices are connected directly to all other vertices without parallel edges or loops.
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8
Q

Walks

A
  • Starts at one vertex and follows any route to finish at another vertex.
  • You must record the order you visit the edges.
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9
Q

Trails

A
  • A walk with no repeated edges.
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10
Q

Paths

A
  • A walk with no repeated edges or vertices.
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11
Q

Circuit

A
  • A walk with no repeated edges that starts and ends at the same vertex:
    IN SUMMARY:
  • TAKE ANY ROUTE
  • RECORD ROUTE
  • START AND END AT SAME VERTEX
  • NO REAPTED EDGES OR VETRICES
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12
Q

Cycle

A
  • A walk with no repeated edges or vertices that starts and ends at the same vertex.
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13
Q

Eulerian trail

A

Follows every edge of a graph and will exist if it is:
- It is connected
- It has exactly tow vertices that have an odd degree.

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14
Q

Eulerian circuit

A

Follows every edge and starts and ends at the same vertex.
- It is connected
- Has vertices of all even degree.

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15
Q

Hamiltonian path

A
  • Visits every vertex of graph once.
  • Don’t have to start and end at the same vertex.
  • No more than 2 vertices of degree 1.
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16
Q

Hamiltonian cycle

A
  • Visits every vertex of graph.
  • Stars and ends at the same vertex.
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17
Q

Subgraph

A
  • A small part of a large graph that has some of the same vertices and edges as the larger one.
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18
Q

Tree

A
  • A connected graph:
  • No cycles.
  • No loops or edges.
  • The number of edges can be calculated using (n-1), where n i the number of vertices.
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19
Q

Spanning tree

A
  • A connected graph:
  • No cycles.
  • No loops or edges.
  • It is found by counting the no. of vertices (n) and removing enough edges so that there are n-1 edges, where n is the no. of edges and they should connect all vertices.
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20
Q

Prims algorithm

A

A formula for determining the minimum spanning tree of a network.

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21
Q

Bridge

A

-Is an edge in a connected graph, that if removed will cause the graph to be disconnected.

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22
Q

Disconnected graph

A
  • Are graphs that are not connected.
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23
Q

Euler’s formula is?

A
  • v-e+f=2
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24
Q

Order of a matrix is always?

A
  • row X column
25
Q

In a square matrix where is the trailing diagonal

A
  • Top right to bottom left.
26
Q

In a square matrix where is the leading diagonal

A
  • Top left to bottom right.
27
Q

Symmetric matrix

A
  • Square matrix
  • Has leading diagonal
  • The original matrix = transpose …e.g. a=transpose of (a)
28
Q

Zero matrix

A
  • Matrix of any order with all elements as 0’s.
  • It is represented with the symbol (O).
29
Q

Triangular matrix

A

Square matrix.
- Upper: when all the elements below the leading diagonal are 0’s.
- Lower: when all the elements above the leading diagonal are 0’s.

30
Q

Identity Matrix

A
  • Square matrix.
  • Leading diagonal= all 1’s.
  • All other elements except leading diagonal=0.
  • Represented with symbol (I).
  • Anything times the identity matrix is= the same matrix.
31
Q

How to transpose matrix on CAS?

A
  • M-7-2.
32
Q

Rules to add and subtract matrix?

A
  • They must have same order.
33
Q

Scaler multiplication of matrix?

A
  • Instead of writing matrix b+b+b+b, we instead write 4b=4[ matrix]= [ matrix when it has been fully multiplied].
34
Q

Rules to divide matrix

A
  • You cannot divide a matrix and it will give you a value of undefined.
35
Q

Post multiply?

A
  • When it is matrix (A) * summing matrix.
36
Q

Pre-multiply?

A
  • When it is Summing matrix * matrix (A).
37
Q

Summing matrix?

A
  • A row or a column matrix where all the elements are 1 and is used to add all the elements in a matrix and give the answer as a single element.
38
Q

Permutation matrix?

A
  • Also an identity matrix.
  • Has to be square.
  • Only one (1’s) per row.
39
Q

Binary matrix?

A
  • Can be any type of matrix.
  • Only includes (1’s) and (0’s).
  • Can include more than one (1’s) per row.
40
Q

Rules for matrix raised to a power?

A
  • Only a square matrix can be raised to a power.
41
Q

How to find the sum of the number of rows in a matrix?

A
  • post multiply by the summing matrix.
42
Q

How to find the sum of the number of columns in a matrix?

A
  • pre-multiply by the summing matrix.
43
Q

If matrix is symmetrical that means?

A
  • That means that each row has to match the corresponding column
44
Q

How to calculate the total one-step communication links?

A
  • Add all of the elements up in each row, but keep them separate do not add all rows up together.
45
Q

One step communication matrix?

A
  • Draw matrix of the graph/communication.
46
Q

How to find two step communication matrix from one step communication matrix?

A
  • If one step matrix = c, THEN two step matrix= c^2.
47
Q

How to find total of one-step and two-step communication matrix on CAS?

A
  • Define one-step matrix (c).
  • Input into CAS ( c+c^2).
48
Q

A Dominance Matrix can used to represent?

A
  • The result of a competition, argument or conflict between a group of people.
49
Q

On step dominance matrix?

A
  • Draw matrix of the graph/communication.
50
Q

Properties of a one-step dominance matrix?

A
  • Square matrix.
  • Binary matrix.
  • Leading diagonal as (0’s).
  • Not symmetrical.
  • Sum of all elements= the number of games ( win/lose).
51
Q

How to find two-step dominance matrix on CAS?

A
  • Define normal matrix (d).
  • Input into CAS ( d^2).
52
Q

How to find total of one-step and two-step dominance matrix on CAS?

A
  • Define one-step dominance matrix (d).
  • Input into CAS ( d+d^2).
53
Q

A transition matrix represents?

A
  • Movement.
54
Q

In a transition matrix elements in each column will always add up to?

A
  • In a transition matrix elements in each column will always add up to 1.
55
Q

In finace for investement rates we look for the?

A
  • Lokk for the highest effective interest rate and we do this by using the CAS and typing in eff( rate, compounding periods in a year).
56
Q

If there is a loop in a adjacency matrix it is represented as a ?

A
  • ONE(1) in the matrix.
57
Q

How to find inverse matrix by hand?

A
  • A^-1 = 1/ det(a) x [ d -b ]
    [ -c a ]
  • det(a)= a X d - c X d , where matrix a= [ a b ]
    [ c d ]
58
Q

What does it mean if the determent is 0?

A
  • There is not inverse and it is a single matrix.

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