Can a complete graph be a tree?
Consider a graph G that contains the edges {u, v}, {u, w} and {v, w}. What can you say about the sequence ({u, v}, {v, w}, {w, u})?
What is the size of a graph with the following adjacency matrix?
$\begin{pmatrix} 0 & 1 & 0 & 0 \\ 1 & 0 & 1 & 0 \\ 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{pmatrix}$
Let's consider a list with 10 elements. How many elements have to be accessed to reach the 6th element?
We use lists to store the neighbors of vertices of a complete graph of order 25. How many elements do such lists contain?
Imagine that we want to represent a graph containing many vertices in memory. We know that this graph has very few edges. What data structures are adapted?
Consider the following problem: we are given a list of routers and proximities between some of these routers. Each router can be associated with one frequency, with the limit that two routers that are in proximity should not be associated with the same frequency. The aim is to find the minimum number of distinct frequencies that have to be chosen in order to solve the problem. What would be the good way to go about solving this problem?