University of Veterinary & Animal Sciences, Pattoki
math
MATH 322

Spring 2016
1
Graph Theory
Begin at the beginning, the King said, gravely, and go on till you
come to the end; then stop.
Lewis Carroll, Alice in Wonderland
The Pregolya River passes through a city once known as Konigsberg. In the 1700s
seven bridges were situated a
University of Veterinary & Animal Sciences, Pattoki
math
MATH 322

Spring 2016
GRAPH THEORY
Keijo Ruohonen
(Translation by Janne Tamminen, KungChung Lee and Robert Pich)
2013
Contents
1
1
6
10
14
18
I DEFINITIONS AND FUNDAMENTAL CONCEPTS
1.1 Definitions
1.2 Walks, Trails, Paths, Circuits, Connectivity, Components
1.3 Graph Operatio
University of Veterinary & Animal Sciences, Pattoki
math
MATH 322

Spring 2016
Lecture Notes on Graph Theory
Vadim Lozin
1
Introductory concepts
A graph G = (V, E) consists of two finite sets V and E. The elements of V are called the
vertices and the elements of E the edges of G. Each edge is a pair of vertices. For instance,
V = cf
University of Veterinary & Animal Sciences, Pattoki
math
MATH 322

Spring 2016
Classroom Presenter Project
CSE 421
Algorithms
Richard Anderson
Lecture 3
Understand how to use Pen Computing to
support classroom instruction
Writing on electronic slides
Distributed presentation
Student submissions
Classroom Presenter 2.0, started
University of Veterinary & Animal Sciences, Pattoki
math
MATH 322

Spring 2016
Who was Dijkstra?
What were his major contributions?
CSE 421
Algorithms
Richard Anderson
Lecture 9
Dijkstras algorithm
Single Source Shortest Path
Problem
Edsger Wybe Dijkstra
http:/www.cs.utexas.edu/users/EWD/
Given a graph and a start vertex s
Determ
University of Veterinary & Animal Sciences, Pattoki
math
MATH 322

Spring 2016
Graph Theory
MAT230
Discrete Mathematics
Fall 2015
MAT230 (Discrete Math)
Graph Theory
Fall 2015
1 / 72
Outline
1
Definitions
2
Theorems
3
Representations of Graphs: Data Structures
4
Traversal: Eulerian and Hamiltonian Graphs
5
Graph Optimization
6
Plana