Homework assignments
(MATH 3116-001, Fall 2025)
Instructor: Gábor Hetyei Last update: Thursday, August 28, 2025

Disclaimer: The information below comes with no warranty. If, due to typographical error, there is a discrepancy between the exercises announced in class and the ones below, or this page is not completely up to date, the required homework consists of those exercises which were announced in class. Check for the time of last update above. If, by my mistake, a wrong exercise shows up below, I will allow you extra time to hand in the exercise that was announced in class. If, however, exercises are missing because this page is not up to date, it is your responsibility to contact me before the due date. (No extra time will be allowed in that case.) This page is up to date if the last update happened after the last class before the next due date.

The deadlines do not apply to the Bonus questions, which expire only once we solve them in class, or on November 27 at latest.

Notation: 5.1/8a means exercise 8, part a, in chapter 5, section 1.

No. Date due: Problems:
1 Tue Sep 2 at noon 1.1/2ab, 6a (just give an example), 8, 16a;   1.2/2, 6bfh;   1.3/2,6.
Bonus questions:
  1. Describe a matrix computation that uses the adjacency matrix of a simple graph to decide whether the graph is connected. (B01, 5 points)
  2. Prove that the edge graph of the n-dimensional hypercube is bipartite. (The vertices of the n-dimensional hypercube are all binary strings of length n, two vertices are adjacent when exactly one of their coordinates differs.) (B02, 5 points)
  3. Describe in terms of the adjacency matrix, when are two simple graphs isomorphic (B03, 3 points).
  4. The Petersen graph is shown in the picture below.
    Show that the Petersen graph may also be defined as the graph whose vertices are all 2-element subsets of {1,2,3,4,5} with an edge connecting {i,j} and {k,l} exactly when {i,j} and {k,l} are disjoint. (B04, 5 points)