TENTATIVE SCHEDULE - SPRING 2013
Topics and times are tentative and subject to change.
1. Introduction to Graph Theory
2. Basics, Special Graphs, Graph Operations
3. Degree Sequences, Regular Graphs, Existence Proof
4. Connected, Disconnected, Walks, Trai
Degrees
Degree
Maximum degree, minimum degree
Endvertex, isolated vertex
First theorem and corollary
The degree of a vertex v V (G), denoted degG (v), is the number of
its neighbors, that is, the number of edges incident to v.
even or odd
endvertex, l
HOMEWORK 1
1. Draw the graph with vertex set V = cfw_v1 , v2 , v3 , v4 and edge set E = cfw_v1 v2 , v1 v4 , v2 v4 .
2. Give the adjacency matrix of the graph in problem 1.
3. One of the primary activities of an applied mathematician is modelling. In a
ma
MATH 4347/5347: Introduction to Graph Theory
Syllabus, Spring, 2013
Instructor: Dr. Teresa Haynes
Office: 307A Gilbreath
Office Hours: TBA
Other times by appointment.
Phone: (423) 439-6960
E-mail: [email protected]
Text: Introduction to Graph Theory, by Gar
1
Isomorphic graphs
The graphs G1 and G2 of Figure 1 are isomorphic (we can
morph (draw) G2 into (to look like) G1 ).
G1 :
u1
v1
s
@
@
@
s
s
w1
@
@
w2
G2 :
@s
x1
s
A
A
s A
x
@2 A
@A
s
@As
u2
v2
Figure 1: Isomorphic graphs.
Two graphs often have the sam
When are Two Graphs the Same?
In every area of mathematics, it is important to know whether two objects
under investigation are the same (in some sense) or are different. For
example, the numbers 2 and 6/3 are considered to be the same, or equal, but
they
Be reading Chapters 1-3 in text.
1
Paths, Cycles
Definitions. Let u and v be two (not necessarily distinct) vertices of
a graph G. A u-v walk in G is a finite, alternating sequence of vertices
and edges that begin with the vertex u and ends with the verte
Graph Theory Homework
Due: February 5, 2013
1. Show that the graphs F1 and F2 are isomorphic by proving the existence
of an isomorphism from F1 to F2 or of an isomorphism from F2 to F1 .
u1
v1
u2
v2
t
t
t
H
H
F1 :
F2 :
t
t
w1
x1
t
H
H
H
H
Ht
t
H
w2
x2
2
What is a Graph?
In this course, we will study mathematical objects called graphs. Often,
when the word graph is used in a mathematical setting, people think pie
charts, bell curves, and bar charts. The word graph is often short for graph
of a function.
C