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-
Math 485, Graph Theory, Fall 2016
Homework #6
Due on Friday, October 28th, 2016.
Problem 1. Do problem 5.34, page 129 of the textbook.
Problem 2. Do problem 5.36, page 130 of the textbook.
Solution: A
Math 485, Graph Theory, Fall 2016
Homework #3
Due on Monday September 26th, 2016.
Problem 1. List all possible non-isomorphic graphs of order 6 and size 13. Hint: Recall that H ' G if and
' G.
It ma
Math 485, Graph Theory, Fall 2016
Homework #4
Due on Monday October 3rd, 2016.
Problem 1. Do problem 4.27 from the textbook.
Problem 2. Do problem 4.37 from the textbook.
Problem 3. Use the matrix tre
Math 485, Graph Theory, Fall 2016
Homework #7
Due on Friday, November 4th, 2016.
Problem 1. Do problem 6.10, page 150 of the textbook.
Solution:
Problem 2. Do problem 6.11, page 150 of the textbook.
7
Some solutions to the collection of problems #1
Math 428 - Solutions torReview problems #1,3,5,6,7,9 for Exam #1 - October 9, 2009
#1 G is a connected graph of order n in which every trail is a path.
Math 485, Graph Theory, Fall 2016
Homework #10
Due on Friday, December 9th, 2016.
Problem 1. Do problem 10.2 on page 278 of the textbook.
Solution:
Problem 2. Do problem 10.6 on page 278 of the textbo
Math 485, Graph Theory, Fall 2016
Homework #2
Due on Monday September 12th, 2016.
Problem 1. Let G = (V, E) be a simple graph. Prove that the shortest path distance dG (x, y) satisfies the triangle in
Math 485, Graph Theory, Fall 2016
Homework #8 Due on Wednesday, November 16th, 2016.
Problem 1. Do problem 8.4, page 193 of the textbook.
SOLUTIONS, Problem Set 11, Math 428, Fall 2007
Solution:
8.4.
Exercise sheet 5: Solutions
Caveat emptor: These are merely extended hints, rather than complete solutions.
Math 485, Graph Theory, Fall 2016
Homework #9
Due on Friday, December 2nd, 2016.
Problem 1.1
Some solutions to the midterm problems
1. (15 points) Let G = K4,3 be the complete bipartite graph with partite sets V1 = cfw_a, b, c, d and V2 = cfw_e, f, g.
(a) (5 points) Find a b-f path of maximal
Math 485, Graph Theory, Fall 2016
Homework #5
Due on Friday, October 14th, 2016.
Problem 1. Prove that if v is a cut vertex of G, then it is not a cut vertex of the complement graph G.
Solution:
Probl
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
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
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.
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 wi
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
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 We
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
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 exer
Math 485: Graph Theory
Outline of Topics for Final Exam
Stephen G. Simpson
305 McAllister, 863-0775
[email protected]
December 14, 2009
The nal exam will include material from the following section
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 gr
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 t
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
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
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 ve