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  1. Print the notecards
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  3. Cut out the notecards by cutting along each horizontal dotted line
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  1. Verify Front of pages is selected for Viewing and print the front of the notecards
  2. Select Back of pages for Viewing and print the back of the notecards
    NOTE: Since the back of the pages are printed in reverse order (last page is printed first), keep the pages in the same order as they were after Step 1. Also, be sure to feed the pages in the same direction as you did in Step 1.
  3. Cut out the notecards by cutting along each horizontal and vertical dotted line
To print: Ctrl+PPrint as a list

17 notecards = 5 pages (4 cards per page)

Viewing:

DECISION 2.1 Modelling with graphs

front 1

graph

back 1

Points (called vertices or nodes) which are connected by lines (edges or arcs)

front 2

weighted graph/network

back 2

if a graph has a number associated with each edge (usually called its weight) then it is a weighted graph or a network

front 3

vertex set

back 3

list of all the nodes on a graph

e.g. A,B,C,D,E

front 4

edge set

back 4

list of all the edges in a graph (AB, AC, etc...)

front 5

subgraph

back 5

A subgraph of (e.g.) graph G is a graph where each of whose vertices belongs to G - it is simply a part of the original graph

(graph on left is graph G, graphs on right are subgraphs of graph G)

front 6

degree/valency/order of a vertex

back 6

number of edges incident to that vertex

if a vertex has even degree we say it is even and if it has odd degree we say it is an odd vertex

front 7

walk

back 7

a route through a graph along edges from one vertex to the next

front 8

path

back 8

a walk in which no vertex is visited more than once

front 9

trail

back 9

a walk in which no edge is visited more than once

front 10

cycle

back 10

a walk in which the end vertex is the same as the start vertex and no other vertex is visited more than once

front 11

Hamiltonian cycle

back 11

a cycle* which includes every vertex

*cycle=a walk in which the end vertex is the same as the start vertex and no other vertex is visited more than once

front 12

in terms of the diagram, give examples of:

1. a walk

2. a path

3. a trail

4. a cycle

5. an hamiltonian cycle

back 12

walk: e.g. RSUWVU, SUV, etc

path: RSUVW, RUVW, etc

trail: RUSVUW

cycle: RSUR

hamiltonian cycle: RSUVWTR

front 13

connected vs unconnected graphs

back 13

Two vertices are connected if there is a path between them. a graph is connected if all its vertices are connected

front 14

loop

back 14

an edge that starts and finishes at the same vertex

front 15

simple graph

back 15

graph in which there are no loops and there is at most one edge connecting any pair of vertices

front 16

digraph

back 16

if the edges of a graph have a direction associated with them they are known as directed edges and the graph is known as a directed graph (digraph)

front 17

Euler's handshaking lemma

back 17

In any undirected graph, the sum of the degrees of the vertices is equal to 2x the number of edges.

Therefore, the number of odd vertices must always be even (including possibly zero). This result is known as Euler's handshaking lemma.