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MAT1DM Discrete Mathematics

tag 0 Download 3 Pages / 646 Words tag 21-10-2020
  • Course Code: MAT1DM
  • University: La Trobe University
    icon is not sponsored or endorsed by this college or university

  • Country: Australia


Assignments are designed to help you master concepts, solve problems and develop your mathematical communication skills. Considerable weight is given to the way you communicate your answers.

  1. (a) Consider the following two graphs G1 and G2.

There are exactly two difffferent isomorphisms from G1 to G2, say, φ1 and φ2. Find both of

them. Present your solution in the form of a table below.


(b) The graph G3 is not isomorphic to G1. Give an isomorphism

  1. For each of the three graphs below, decide whether or not it is planar. If it is planar, give a plane

drawing, if not, prove its non-planarity using Theorem 4.4.5 and/or Kuratowski’s Theorem 4.4.7.

  1. 1 (a) Using the index laws, write:

(b) Number the functions 1 → 5 from slowest to fastest, for long term growth.

  1. Use the lazy c method to show that:
  1. (a) Find suitable values of n : n ∈ N, so that the following inequalities are true.

(b) Find a value of n so that the four inequalities in part (a) hold simultaneously.

(c) Use your answer to (b) prove

with a choice of c = 3

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