Discrete Mathematics for Computer Science Managing Information Systems Formulate Hypothetical Research Designs Activity Conclusi…

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MAT2DMX – Discrete Mathematics for Computer Science
Assessment 3 – Graph algorithms, algorithm analysis, finite state machines
(30 marks)
Task weighting: 15%
Assessment Objectives
▪ Analyse graphs and some applications in computer science.
▪ Analyse algorithms arising in computer science and understand basic mathematical
model of computation.
This is an INDIVIDUAL assignment. Students are not permitted to work in a group
when writing this assignment.
Copying, Plagiarism
This is an individual assignment. Students are not permitted to work in a group when writing
this assignment. Plagiarism is the submission of another person’s work in a manner that
gives the impression that the work is their own. La Trobe University treats plagiarism
seriously. When detected, penalties are strictly imposed.
Further information can be found on http://www.latrobe.edu.au/students/academic
integrity/explanation/plagiarism.
Submission Guidelines
• Your assignment submission should be in Word document (A4 size). Drawing of
graphs, gates, … can be used as pictures and pasted into assessment file.
• Submit the electronic copy of your assignment through the subject LMS.
• Late submission: Submission after the deadline will incur a penalty of 5% of the
available marks for that task per day capped at 5 days. No assignment will be
accepted after 5 days. If you have encountered difficulties that lead to late
submission or no submission, you should apply for special consideration.
Submitting your assignment
When you have completed your answers, submit the assessment on the Learning Portal.
You should submit the following:
• Submit your answers in a Word document called xxx_MAT2DMX_Assessment3 (where
xxx is your student ID number).
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Graphics:
Graphics can be done with hand drawing and insert into assessment answer. For example,
students can draw on a paper and take a photo, then paste into word file.
Assignment structure
There are 11 questions. Topics are covered in weeks 7 – 10.
Question 1 (4 marks):
In each case below, either draw a tree or graph with the required properties or prove that it does
not exist.
(a) A tree on 8 vertices with degrees 1, 1, 1, 1, 1, 2, 3, 4.
(b) A tree on 6 vertices with degrees 1, 2, 3, 2, 2, 2.
(c) A connected graph on 5 vertices with degrees 2, 3, 3, 5, 5.
(d) A connected graph on 7 vertices with degrees 2, 2, 3, 4, 4, 4.
A graph can have multiple edges or loops.
(Explanation marks are for correct draw or correct explanation. If you can draw, you do not need
to explain. See Section 7.6 in Week 7 handout for examples and theory.)
Question 2 (2 marks):
State which of the following graphs are planar. For those which are planar, give a planar graph
drawing. For those which are not planar, explain why they are not. (For reference, see Section
7.5 and Week 7 practical exercises.)
(a) (b)
Graph

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