Math 485, Graph Theory: Midterm Exam
Stephen G. Simpson
Monday, November 9, 2009
Solutions
1. (a) If G is a k -regular graph with n vertices, how many edges does G
have?
Solution. kn/2, by the degree-sum formula.
(b) Draw a 3-regular graph with 11 vertice
Math 485 Homework 10 Fall 2007 Due: Friday, November 30
In all the problems, indicate how you arrived at your answer and explain your work. 1. Prove or disprove: Every vertex cover of a graph contains a minimum vertex cover. 2. Prove or disprove: Every tr
Math 485 Homework 6 Fall 2007 Due: Friday, October 19
In all the problems, indicate how you arrived at your answer and explain your work. 1. We proved in class that the center of a tree is a single vertex or a single edge. (a) (5 points) Find an example o
Math 485 Homework 7 Fall 2007 Due: Friday, October 26
In all the problems, indicate how you arrived at your answer and explain your work. 1. Determine (G) for the following graphs using the recursive algorithm. (a) (b) 2. For m 1, determine (K2,m ). 3. Le
Math 485 Homework 3 Fall 2007 Due: Friday, September 21
In all the problems, indicate how you arrived at your answer and explain your work. 1. For each n 1 define the following graph Hn : The vertices of Hn are n-tuples whose entries are either 0 or 1. Tw
Math 485 Homework 4 Fall 2007 Due: Friday, September 28
In all the problems, indicate how you arrived at your answer and explain your work. 1. (a) How many subgraphs does Kn have that are isomorphic to the n-cycle Cn ? (b) How many subgraphs does Kn,n hav
Math 485, Graph Theory: Final Exam
Stephen G. Simpson
Monday, December 14, 2009
13 problems, 220 points
1. (15 points) Draw a simple connected planar graph which is 6-regular, or
prove that no such graph exists.
2. (15 points) Exhibit a planar graph G whi
Math 485: Graph Theory
Outline of Topics for Final Exam
Stephen G. Simpson
305 McAllister, 863-0775
simpson@math.psu.edu
December 14, 2009
The nal exam will include material from the following sections in the West
textbook: 1.1, 1.2, 1.3, 1.4, 2.1, 2.2, 2
Math 485, Graph Theory: Homework #1
Stephen G. Simpson
Due Wednesday, September 9, 2009
The assignment consists of exercises 12, 13, 14, 20, 22, 25, 26 on pages 1418
of the textbook by West. Each exercise counts for 10 points. Here are some
(rather sketch
Math 485, Graph Theory: Homework #2
Stephen G. Simpson
Due Wednesday, October 5, 2009
The assignment consists of Exercises 1.2.8, 1.2.20, 1.2.21, 1.2.30, 1.3.21,
1.3.24, 1.3.26, 1.4.11, 1.4.14, 1.4.18, 1.4.22, 1.4.27 of the textbook by West.
Each exercise
Math 485, Graph Theory: Homework #3
Stephen G. Simpson
Due Monday, October 26, 2009
The assignment consists of Exercises 2.1.29, 2.1.35, 2.1.37, 2.2.18, 2.3.8,
2.3.10, 2.3.13, 2.3.14, 2.3.15 in the West textbook, plus the following, where Ln
is the n-ladd
Math 485, Graph Theory: Homework #4
Stephen G. Simpson
Due Friday, December 4, 2009
The assignment consists of Exercises 3.1.8, 3.1.19, 3.1.24, 3.1.25, 3.2.6, 6.1.12,
6.1.25, 6.1.35, 6.2.6 in the West textbook. Each exercise counts for 10 points.
Here are
Math 485, Graph Theory: Midterm Exam
Stephen G. Simpson
Monday, November 9, 2009
8 problems
1. (a) If G is a k -regular graph with n vertices, how many edges does G
have?
(b) Draw a 3-regular graph with 11 vertices or prove that no such graph
exists.
2. R
Math 485: Graph Theory
Outline of Topics for Midterm Exam
Stephen G. Simpson
November 2, 2009
The midterm exam will include material from the following sections in the
West textbook: 1.1, 1.2, 1.3, 1.4, 2.1, 2.2, 2.3, 3.1, 3.2.
1.1. basic concepts
(a) ver
Math 485, Graph Theory, Fall 2016
Homework #1
Due on Friday September 2nd, 2016.
Problem 0. Read pages 1-12 and 19-32 of the textbook.
Problem 1. Give examples or prove that no such examples exist:
(a) A graph G such that each vertex is adjacent to exactl