This Assignment is compulsory, and contributes 10% towards your nal grade in Math2302,
8.5% in Math7308. The due date for the assignment is 10am on Monday 25 October, 2021 (see
the ECP for information about requesting an extension). You should submit your assignment
electronically. Prepare your assignment as a PDF le, either by typing it or by scanning your
handwritten work. Ensure that your name, student number and tutorial group number appear
on the rst page of your submission. Check that your pdf le is legible and that the le size is
not excessive. Files that are poorly scanned and/or illegible may not be marked. Upload your
submission using the assignment submission link.
- For each of the graphs shown below, either prove that the graph is Hamiltonian or prove that the graph is not Hamiltonian. You may use the fact that the Petersen graph is not Hamiltonian.
( 12 marks)
that the graph is not Hamiltonian.
For a graph $G$, the line graph of $G$, denoted by $L(G)$, has a vertex corresponding to each edge of $G$, and two vertices of $L(G)$ are adjacent if and only if their corresponding edges are adjacent in $G .$ Let $P$ be the Petersen graph. Determine each of the following and justify your answers. You may use properties of the Petersen graph that were proven in class.
( 10 marks)
(a) $\beta(L(P))$
(b) $\sigma(L(P))$
(c) $\omega(L(P))$
(d) $\chi(L(P))$
(e) $\chi^{\prime}(L(P))$
Use Dijkstra’s algorithm to determine the distance from $A$ to each other vertex in the weighted graph shown below, and state a shortest path from $A$ to $J$.
(8 marks)
MATH2302 – Discrete Mathematics II: Theory & Applications
| Lecturer | Associate Professor Diane Donovan |
| Course Link | UQ Site |
| Faculty | Science |
| Prerequisites | MATH1061 |
| Contact Hours | 3L 1T |
| Semester(s) Taught | Semester 2 |
| Course Units | 2 |
90.3/100Learning Materials ( 86 )Learning Activities ( 100 )Blackboard Management ( 94 )Course Content ( 100 )Course Structure ( 79 )Contact Availability ( 88 )Course Difficulty ( 85 )
This is a qual course, fairly pure but that’s what you wanted, right?
Resources: no textbook, just good course notes. Just studying these notes would be enough for the midsem but I’d give the leccy’s a go before the final. More examples in the notes would be nice so I hope over time they expand it.
My main issue isn’t with this course exactly, but that I was hoping for some more advanced logic after MATH1061, to lead into higher level set theory courses [there’s no 2nd year logic and set theory courses]. The topology was real dece since the only other time you’ve seen it is in an analysis course.
If you’re shakey on math1061 content some areas might be a bit rough.
This isn’t a write-off easy course.
It might seem a bit weird that Math2301 and Math2302 both have bits about group theory… it feels just a little inefficient.
I’ve always been worse with permutations, combinations and counting, so I didn’t really rate that part of the course but I can appreciate that some people love their combinatorics. The graph theory is beautiful, since isn’t too much or too little, and this course would lead nicely into third year courses.
If it were up to me, i’d throw in a whole bunch of tiny, miscellanious maths, recreational bits, everything you might see in a popular science book, or it’d be nice if the lecturers could pose some interesting questions, tell you what’s still open in mathematics, give you a bigger picture, etc.
The difficulty is mostly conceptual, and just getting familiarity. You just practice a lot and you’ll be right, doesn’t feel unfair. If you know your stuff it’s actually pretty easy but you’ve got to work for it.Semester taken
Semester 1 – 2017Your program/major
BSc, Math and Physics MajorIs lecture attendance necessary?
The lectures are worth itIs the textbook necessary?
What\’s a textbookPositives
- MATH1061++
- Fun content
- Bridge for higher graph theory courses
Negatives
- Overlaps with Math2301 a little??
- Notes aren’t always enough to learn from
- Lots of math1061 knowledge expectd
