Graph theory - the study of graphs and networks, is often considered part of combinatorics, but has grown large enough and distinct enough, with its own kind of problems, to be regarded as a subject in its own right.[12] Graphs are one of the prime objects of study in discrete mathematics. They are among the most ubiquitous models of both natural and human-made structures. They can model many types of relations and process dynamics in physical, biological and social systems. In computer science, they can represent networks of communication, data organization, computational devices, the flow of computation, etc. In mathematics, they are useful in geometry and certain parts of topology, e.g. theory. Algebraic has close links with group theory. There are also continuous graphs, however for the most part research in graph theory falls within the domain of discrete mathematics. Combinatorics -studies the way in which discrete structures can be combined or arranged. Enumerative combinatorics concentrates on counting the number of certain combinatorial objects - e.g. the twelvefold way provides a unified framework for counting permutations, combinations and partitions. Analytic combinatorics concerns the enumeration (i.e., determining the number) of combinatorial structures using tools from complex analysis and probability theory. In contrast with enumerative combinatorics which uses explicit combinatorial formulae and generating functions to describe the results, analytic combinatorics aims at obtaining asymptotic formulae. Design theory is a study of combinatorial designs, which are collections of subsets with certain intersection properties. Theory studies various enumeration and asymptotic problems related to integer partitions, and is closely related to q-series, functions and orthogonal polynomials. Originally a part of number theory and analysis, partition theory is now considered a part of combinatorics or an independent field. Order theory is the study...

...LAB # 1
Graph Matching
Principles of Physics I Laboratory
Breanna Wilhite
Introduction
In this lab motion will be represented by graphs that plots distance and velocity vs. time. A motion detector will be used to measure the time it takes for a high frequency sound pulse to travel from the detector to an object and back. By using this method sound can determine the distance to the object, or its position. This device will determine in what direction the...

...Introduction in GraphTheory
(BASIC CONCEPTS)
BASIC CONCEPTS
We used decision trees in Unit DT and used them to study decision making. However,
we did not look at their structure as trees. In fact, we didn’t even define a tree precisely.
What is a tree? It is a particular type of graph, which brings us to the subject of this unit.
What is a Graph?
There are various types of graphs, each with its own...

...objective of line graphs is to define raw data, making it easily understandable with a visual representation. By plotting data on a line graph, you assign it a vertical and horizontal value that corresponds to the raw data determining the graph. For instance, if tracking annual sales at a retail store, the data would be defined by the amount of sales in dollars and the months during which these sales took place.
Interpreting Data
The visual...

... |
1. Name three different kinds of graphs that are often used to plot information and discuss the value of each.
Answer:
Three types of graphs are line graph, histogram or bar graph, and pie chart graph.
The line graph is used to describe how an object moves explaining relationship between time and distance traveled.
A histogram or bar graph is used to compare quantities...

...Locus of Parabola
going through an equation......
while b is varied and the variables a and c are held constant. So let's start with the graph where all variables, a, b and c, are equal to 1.
The graph opens upward because a is postive. If a was negative the graph would open in the negative direcction. It is not symmetrical around the y-axis because c = 1. Because c = 1, when x = 0, the parabola passes through the point (0,...

...line on a Cartesian graph is approximately the distance y in feet a person walks in x hours. What does the slope of this line represent? How is this graph useful? Provide another example for your colleagues to explain.
The slope of the line represents the speed of the person in feet per hour. This graph is useful because it provides a visual representation of the continuous motion of the person walking, something that could not provided by something...

...Graphs - Introduction
Terminology
Graph ADT
Data Structures
Reading: 12.1-12.2
COSC 2011, Summer 2004
Definition
• A graph is a pair (V, E), where
– V is a set of nodes, called vertices
– E is a collection of pairs of vertices, called edges
• Both are objects (i.e. store data)
G
E
B
F
A
Vertex
city
computer
web page
airport
C
D
COSC 2011, Summer 2004
H
Edge
road
cable
hyperlink
flight
Example Applications
•
•
•
•
•
Electronic circuits...

...GraphTheoryGraphsGraph:- A graph consists of a nonempty set of points or vertices, and a set of edges that link together the vertices. A simple real world example of a graph would be your house and the corner store. Where the house and the store are the vertices and the road between them is the edge connecting the two vertices.
Or a graph is a network consisting of vertices (or nodes)...