1.1 How many simple graphs are there of four vertices? Draw all of them. 1.2 Deduce the number of simple graphs with n vertices. Draw a graph modeling the relationships between the following Wikipedia...

Extracted text: 1.1 How many simple graphs are there of four vertices? Draw all of them. 1.2 Deduce the number of simple graphs with n vertices. Draw a graph modeling the relationships between the following Wikipedia articles: Chile, Latin America, Beer, Mexican cuisine, and Olive oil. Is this graph dense or sparse? 1.3 1.4 The routing network of German cities below shows that each pair of distinct cities are con- nected by a flight path. The weight of each edge is the flight distance in kilometers between the two corresponding cities. In particular, there is a flight path connecting Karlsruhe and Stuttgart. What is the shortest route between Karlsruhe and Stuttgart? Suppose we can remove at least one edge from this network. How many possible ways are there to remove edges such that, in the resulting network, Karlsruhe is no longer connected to Stuttgart via a flight path? Karlsruhe 197 Augsburg Mannheim 57 72 Munich 383 Kassel 145 Frankfurt 149 97 Nuremberg 90 Würzburg 157 154 Stuttgart Erfurt